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I
G«T
GIFT OF
Mrs , Dwayne Young
Th
r— *^H
-i=
:^-^' ^ /"i
■'^/Py^^ /iAtJ^
The Principles Underlying
Radio Communication
RADIO PAMPHLET No. 40
December 10, 1918
Signal Corps, U. S. Army
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Washington : Government Printing Office : 1919
' 1 •
War Department
Office of the Chief Signal OflScer
GIFT c
•••
•••
• • • •
• • • • •
• • • • •
•• • ••
• • • •
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to «<*
• • •
• • ••
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• • •
• • • • • t •
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THE PRINCIPLES UNDERLYING RADIO
COMMUNICATION.
Prepared by the Bureau of Standards under the direction of
the Office of the Chief Signal Officer of the Army, Training
Section.
Ackrwwledgmerd is made of the valuable service rendered the
Signal Corps by the Bureau of Standards through the icork of
Dr. J. H. Bellinger and the following men engaged with him in
the writing of this book:
Dr. F. W. Grover.
Prof. C. M. Smith.
Prof. G. F. WiUig.
Dr. A. D. Cole.
Dr. L. P. Wheeler.
Prof. H. M. Royal
3
17.145474
ADDITIONAL COPIES
OF THIS PUBLICATION MAT BE PROCURED FROM
THE SUPERINTENDENT OF DOCUMENTS
GOVERNMENT PRINTING OFHCE
WASHINGTON, D. C.
AT
66 CENTS PER COPY
V
PREFACE.
In this book are presented briefly the basic facts
and principles of electromagnetism and their applica-
tion to radio communication. In the eflFort to present
these topics in a simple manner for students with very
little mathematical preparation, it has been necessary
at times to use definitions, illustrations, and analogies
which would not be used in a work prepared for more
advanced students. Frequent references to standard
books are given for further study, and students should
be encouraged, as far as possible, to consult them.
5
- * « « • ,•, • • •
TABLE OF CONTENTS.
Introduction.
Page.
1. What radio communication means 15
2. Fundamental ideas of electric circuits 16
Chapter 1. Elementary Electricity.
A. Electric Current.
3. Effects of electric current 23
4. Magnitude and direction of current 24
5. Measurement of electric current and quantity of elec-
tricity 25
6. Electrons 26
B. Resistance and Resistivity.
7. Resistance and conductance 27
8. Resistivity and conductivity 28
9. Temperature coefficient 30
10. Current control 31
11. Conducting materials 32
12. Non-conducting or insulating materials 34
C. Potential Difference, Emf., and Ohm's Law.
13. The meaning of emf 36
14. Ohm's law 38
15. Sources of emf 42
16. Internal voltage drop and line drop 46
D. Batteries.
17. Kinds of cells 49
18. Simple primary cell 49
19. Types of primary cells 51
20. Dry cells 52
21. Storage cells 53
22. Internal resistance in batteries 59
7
• • «
8
• • •
• • •
• •••
« • • •
• • •
• • •
• • •
.•••••
• •• •
• * • •
• • •
*ABLE OF CONTENTS,
II I /.^- Electric Circuits.
23. Current flow requires a complete circuit. .
24. Series and parallel connections
25. Divided circuits. The shunt law
26. The potentiometer"
27. The Wheatstone bridge
28. Heat and power losses
F. Capacitance.
29. Dielectric current
30. Condensers
31. Dielectric properties
32. Types of condensers
33. Electric field intensity
34. Energy stored in a condenser
35. Condensers in series and in parallel
G. Magnetism.
36. Natural magnets
37. Bar magnets
38. The magnetic field
39. Magnetic flux and flux density.
40. The magnetic field about a current
41. The solenoid and the electromagnet
42. Magnetic induction and permeability
43. The force on a current in a magnetic field.
H. Inductance.
44. The linking of circuits with lines of magnetic flux
45. Induced electromotive force
46. Self inductance
47. Mutual inductance
48. Energy relations in inductive circuits
I. Alternating Current.
49. Reactance
50. Nature of an alternating current
51. Average and effective values of alternating current
52. Circuit with resistance only
53. Phase and phase angle
54. Alternating current in a circuit containing inductance
only
Page.
60
61
66
67
69
70
71
72
74
76
77
78
79
81
81
82
83
84
84
85
86
87
88
90
91
92
93
93
95
97
97
98
TABLE OF CONTENTS. 9
Pag«.
55. Circuit containing inductance and resistance 100
56. Charging of a condenser in an alternating current circuit. 102
57. Circuit containing capacitance, inductance, and resist-
ance 104
58. The alternating current transformer 105
m
J. Measuring Instruments.
59. Hot wire instruments 106
60. Magnetic instruments ; 108
Chapter 2. Dynamo-Electric Machinery.
61. Generators and motors 115
A. The Alternator.
62. Production of emf . by revolving field 115
63. Direction of emf 117
64. Emf. curve 117
65. Cycle, period, frequency 117
66. Multipolar magnets 118
67. Field and armature 118
68. Coil-wound armature 119
69. Concentrated and distributed windings 121
70. Magnetic circuit 121
71. Field excitation 124
72. Stator and rotor 125
73. Arrangement of parts 125
74. Other forms of alternator 125
75. Polyphase alternator 128
B, Alternator Theory, Losses, etc.
76. Equations for frequency and emf 132
77. Dependence of driving power on current 131
78. Losses 133
79. Rating. Name plate data 135
80. Efficiency 136
81. Regulation 136
82. Armature impedance and armature reaction 137
83. Effect of power factor on regulation 137
84. Effect of speed on regulation 138
85. Voltage control 138
10 TABLE OF CONTENTS.
C. Direct Current Generators.
Page.
86. Commutation 138
87. Ring and drum winding 141
88. Separate excitation, series, shunt, compound 144
89. Characteristics of terminal voltage 146
90. Emf . equation 148
91. Voltage control 149
92. Effect of varying speed 149
D. Special Alternators for Kadio Uses.
93. Audio frequency and radio frequency 149
94. Audio frequency generators 150
95. Badio frequency generators 161
E. Motors.
96. Uses of d. c. and a. c. motors 164
97. D.c. shunt motor 164
98. D.c. series motor 172
99. Other d.c. motors 173
100. Combination a.c. and d.c. motors 173
101. Induction motors 173
F. Motor-Generators and Dynamotors.
102. Motor-generators 175
103. Rotary converters. 177
104. Dynamotors 177
105. Double current generators 178
106. Common troubles 179
Chapter 3. Radio Circuits.
A. Simple Radio CiRcurrs.
107. The simplicity of radio theory 182
108. The simple series circuit 183
109. Series resonance 185
110. Tuning the circuit to resonance 190
111. Resonance curves 191
112. The wavemeter 193
113. Parallel resonance 195
114. Capacitance of inductance coils 199
TABLE OF CONTENTS. 11
B. Damping.
Page.
115. Free oscillations 200
116. Frequency, damping, and decrement 205
C. Resistance.
117. Resistance ratio of conductors 208
118. Brush, spark, dielectric, and radiation resistance 21]
D. Coupled Circuits.
119. Kinds of coupling 212
120. Double hump resonance curve 214
121. Forced oscillations 216
122. Free oscillations of coupled circuits with small damping. 218
123. Impulse excitation. Quenched gap 221
Chapter 4. Electromagnetic Waves.
A. Wave Motion.
124. Three ways of transmitting energy'- 223
125. Properties of wave motion 223
126. Wave trains, continuous and discontinuous 224
B. Propagation op Waves.
127. Waves propagated by elastic properties of medium 225
128. Properties of electromagnetic waves 225
129. Modification of waves in free space near earth 226
130. Static 228
C. Theory op Production and Reception op Electromagnetic
Waves.
131. Magnetic field produced by moving lines of electric dis-
placement 229
132. Mechanism of radiation from a simple oscillator 230
133. Action in receiving 232
D. Transmission Formulas.
134. Statement of formulas 234
135. Examples of use 235
136. General deductions 235
12 TABLE OF CONTENTS.
E. Device for Radiating and Receiving Waves.
Page.
137. Description of the antenna 236
138. Different types 238
139. Current and voltage distribution in an antenna 239
140. Action of the ground. Counterpoises 240
F. Antenna Characteristics.
141. Capacitance 242
142. Inductance 243
143. Resistance 243
144. Wave length and its measurement 244
145. Harmonics of wave length 246
146. Directional effect 246
G. Antenna Construction.
147. Towers and supports 247
148. Insulators 247
149. Antenna switch. Conductors 248
150. Grounds and counterpoises 249
H. Closed Coil Aerials.
151. Directional curve 250
152. Constants of closed coil aerials 251
Chapter 5. Apparatus for Transmission and Reception (Exclusive
of Vacuum Tubes).
A. Apparatus for Damped Wave Transmission.
153. Function of transmitting apparatus 254
154. Simple spark discharge apparatus 254
155. Transmitting condensers 257
156. Spark gaps 257
157. Simple induction coil set 262
158. Operation of induction coils from power lines 263
159. Portable transmitting sets 264
160. Simple connections for the production of electric waves. 265
161. Inductively coupled transmitting set 268
162. Direct coupled transmitting set 270
163. Comparison of coupled and plain antenna sets 271
164. Tuning and resonance 272
TABLE OF CONTENTS. 13
Page.
165. Coupling 272
166. Damping and decrement 274
167. Additional appliances 275
168. Adjustmentof a typical set for sharp wave and radiation. 277
169. Efficiency of the set 278
170. Calculations required in design 278
171. Simple field measurements 283
B. Apparatus for Undamped Wave Transmission.
172. Advantages of undamped oscillations 287
173. Use of high frequency alternators 287
174. Arc sets 288
175. Calibration and adjustment of sets 290
C. Apparatus for Reception op Waves.
176. General principles 290
177. Typical circuits for reception of damped waves 293
178. Typical circuits for reception of undamped waves 299
179. Crystal detectors 302
180. Telephone receivers 305
181. Receiving coils and condensers 306
182. Measurement of received current 310
Chapter 6. Vacuum Tubes in Radio Communication.
183. Introduction 311
A. Electron Flow in Vacuum Tubes.
184. Current in a two-electrode tube 31 1
185. Actual forms of two-electrode tubes 314
186. The three-electrode tube 315
187. Effect of grid 317
188. Characteristic curve 317
189. Effect of an alternating emf. applied to grid 319
190. Practical forms of three-electrode tubes 320
B. The Vacuum Tube as a Detector.
191. Simple detector circuit and explanation of its action 322
192. Effect of incoming signals upon the plate current 325
14 TABLE OF CONTENTS.
C. The Vacuum Tube as an Amplifier.
Page.
193. General principle 326
194. Elementary theory of amplification 328
195. Audio frequency amplification , 330
196. Regenerative amplification ^ 330
197. Vacuum tube amplifier with crystal detector 331
D. The Vacuum Tube as a Generator.
198. Conditions for oscillation 332
199. Practical considerations in using vacuum tubes as oscil-
lation generators. . ; 334
200. Tubes suitable for developing considerable power 335
201. Heterodyne and autodyne receiving by vacuum tubes. . 336
E. Radio Telephony.
202. Voice modulation of radio currents by vacuum tubes. . 337
203. Other methods of voice modulation 339
204. Practical use of vacuum tubes in radio telephony 339
Appendices.
Appendix 1. Suggested List op Laboratory Experiments. 342
Appendix 2. Units 350
Appendix 3. Symbols 354
INTRODUCTION.
1. What Badio Communication Means. — In military service all
possible means of communication are used, including the most
primitive. However, the best and most rapid are the electrical
methods. These include the ordinary wire telegraph and telephone
and the wireless or radio apparatus. Without wire connecting lines,
radio messages are sent from one point to another on the battle front,
from ship to shore, across the oceans, to airplanes, and even to
submerged submarines.
When a pebble is thrown into the smooth water of a pond it starts
a series of circular ripples or waves, which spread out indefinitely
with a speed of a few hundredths of a meter^ per second. Similarly,
an electric disturbance starts electric waves, which spread out in
all directions, and travel with the velocity of light, or 300,000,000
meters per second. It is by means of these electric waves that radio
messages are sent.
In order to make use of electric waves for the practical purpose
of sending messages, it is necessary —
(a) To produce regular electric disturbances in a circuit which
start the waves. (These disturbances are electric currents which
reverse rapidly in direction.)
(6) To get the waves out into surrounding space, through which
they travel with great speed. (This is done by means of the trans-
mitting antenna.)
(c) By means of these waves, to set up electric currents in a
receiving circuit at the distant station. (The device which these
waves strike as they come in, and which turns them over to the
receiving circuit, is called the receiving antenna.)
(d) To change these currents so that they may be detected by
electric instruments. (The operator usually receives the message
through signals in a telephone receiver.)
The student of radio communication needs a more thorough
knowledge of electrical theory than that needed for some branches
I The meter and other units are explained in Appendix 2, p. 350.
15
1 6 INTRODUC TION .
of electrical work. This fact needs emphasis for the beginner. Of
course a man can learn to operate and care for apparatus without
having a real understanding of its underlying principles. It only
requires that he have a certain type of memory, industry, and a
little common sense. But a man with only this kind of knowledge
of his subject is of limited usefulness and resourcefulness, and can
not advance very far. The real radio man must have some training
in the whole subject of electricity and magnetism, as well as a rather
intimate familiarity with some restricted parts of it. An under-
standing of radio communication requires some knowledge of the
following subjects:
(a) Direct and alternating currents and dynamo machinery.
(6) High frequency alternating currents, including the subject of
condenser discharge.
(c) Conduction of electric current in a vacuum as well as in wires.
(d) Electric waves, which involves some acquaintance with
modern ideas of electricity and the ether.
(e) The apparatus used for the production and reception of elec-
tric waves.
2. Fundamental Ideas of the Electric Circuit. — It is common
knowledge that a battery supplies what is known as a current of
electricity. To obtain the current there must be a complete closed,
conducting path from the battery through the apparatus which is
to be acted on by the current, and back again to the battery.
For example, when connecting up an electric bell, a wire is
carried from one binding post of the battery (Fig. 1) to one of the
binding posts of the bell, and a second wire is brought from the
other binding post of the bell back to the remaining binding post
of the battery. Any break in the wire immediately causes the cur-
rent to stop and the bell to be silent. This furnishes an easy method
of controlling the ringing of the bell, since it is only necessary to
break the circuit at one point to stop the current, or to connect
across the gap with a piece of metal to start the current going again.
Thus we have the button for accomplishing the act of control, and
the battery supplies the energy required to ring the bell.
Similar considerations apply when we are using the city lighting
circuit. Wires are brought, more or less directly, from the lighting
station to the lamp, and a small break in the path through the socket
is provided. This can be bridged by a metal spring actuated by
the key. Or the opening and closing of the circuit can be accom-
INTRODUCTION.
17
plished by a similar mechanism in the wall of the room, or by a
knife switch (Fig. 2) in a small cupboard.
Sometimes the lamps suddenly go out, and we say that a fuse has
been blown. A short length of wire, through which the current
has been passing, is of an easily fusible metal which has melted
away because too strong a current has been passing. Or it may be
that it has become necessary to open a switch at the power house.
It makes absolutely no difference where the break is made in the
circuit, the result is the same; the current suddenly stops. Elec-
tricity must, then, be regarded as flowing in every part of the circuit.
f=lQ. 1
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Circuit
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A fcaTTery Circoit is liKe A )Di{3«
circuit ^u( I of \MAt«p
SO that electricity is leaving the battery or dynamo at one side,
and coming back to it at the other side.
Current. — ^The current flowing in a circuit is no stronger at one
point of the circuit than at another. This can be proved by con-
necting a measuring instrument called an ammeter into the cir-
cuit at different points, a, 6, or c, Fig. 2. It is found to register
the same at whatever point this test is made. A useful illustration
of the electric circuit is a closed circuit of pipe (Fig. 3) completely
filled with water, and provided with a pump, P, or some other
device for causing the water to circulate. The amount of water
which leaves a given point in each second is just the same as the
amount which arrives in the same length of time. Now in the
electric circuit we have no material fluid, but we suppose that there
97340"— 19 2
18 INTRODUCTION.
exists a substance, which we call electricity. Electricity behaves
in the electric circuit much like an incompressible fluid in a pipe
line. We are very sure that electricity is not like any material
substance which we know, but the common practice among students
and shop men of calling it *' juice" shows that they think of it as
like a fluid. We will, then, imagine the electric current to be a
stream of electricity flowing around the circuit.
One way of measuring the rapidity with which water is flowing
is to let it pass through a meter which registers the total number
of quarts or gallons which pass through. By dividing the quantity
by the time it has taken to pass we obtain the rapidity of flow. There
are instruments by means of which it is possible to measure the total
quantity of electricity which passes any point in the circuit during a
certain time. If we divide this quantity by the time, we obtain
the amount of electricity which has passed in one second. This is a
measure of the current strength.
In practical work, however, the strength of the current is meas-
ured by instruments (ammeters) which show at each moment just
how strong the current is, in somewhat the same manner as we may
estimate the swiftness of a stream by watching a chip on the surface.
This kind of an instrument enables us to tell at a glance what the
current is without the necessity for a long experiment, and further
we may detect changes in the strength of the current from moment to
moment. In this connection it will be remembered that two meas-
uring instruments are to be found on an automobile. The speed-
ometer shows what the speed of the car is at each moment, so that
the driver may know instantly whether he is exceeding the speed
limit, and govern himself as he sees fit. The other instrument shows
how many miles have been covered on the trip, and of course the
average speed may be calculated from its indications, if the length
of the trip has been timed. The instrument for measuring total
quantity of electricity corresponds to the recorder of the total miles
traversed; the ammeter corresponds to the speedometer.
Electromotive Force. — ^The water will not flow in the pipe line.
Fig. 3, unless there is some force pushing it along, as, for example,
a pump, and it cannot be kept flowing without continuing the pres-
sure. Electricity will not flow in a circuit unless there is a battery .
or other source of electricity in the circuit. The battery is for the
purpose of providing an electric pressure. To this is given the name
** electromotive force" — ^thatis, a force which moves the electricity.
INTRODUCTION,
19
This is usually abbreviated to "emf." The larger the number of
cells which are joined in the circuit the greater the electricpressure
and the larger the current produced, just as the rapidity of flow of
the water in the pipe line may be increaaed by increasing the pump
pressure.
Be^tance. — There ia always some friction in pipe, whatever
its size or material, and this hinders the flow of the water to some
extent. If it were not for the friction, the water would increase
indefinitely in speed. Similarly, there is friction in the electric
circuit. This is called the "reaiatance" of the circuit. The greater
the resistance the smaller the current which can be produced in
the circuit by agiven battery, just as the greater the friction the lees
\Q.
Fia.5
J
(
K
K<
^5
p*
it=l^
1?
•±r"
rapid the flow of water with a given pump acling. A resistance coil
at any point in the circuit corresponds to a partially closed valve in
the pipe at any point {Fig. 4).
Steady and VariabU Currents. — A pump producing a steady pres-
sure gives rise to a steady flow of water. Tne same is true of batteries
and certain dynamos which produce a steady emf. A steady
electric current in one direction ia called a "direct current." We
may suppose, however, that the water is given a succession of pushes
all in the same direction, but separated by intervals when the water
is not being pushed. Such a case occurs in the circulation of the
blood by the heart beats. Likewise, a current of this nature may
20 INTRODUCTION.
be produced in a circuit where the emf. acts intermittently. To
such a current the name "pulsating current" is very appropriately
applied.
A very important variety of current for radio work is that known
as '* alternating current." This is analogous to the kind of flow
which would be produced if, instead of being acted on by a pump,
the water were agitated by a paddle which moved back and forth
rapidly over a short distance, without traveling beyond certain
limits. Under this impetus the water no sooner gets up speed in
one direction than it is compelled to slow up and then gather speed
in the opposite direction, and so on over and over again. The water
simply surges, first in one direction, and then in the other, so that a
small object suspended in the water would not travel continuously
around the pipe line, but would simply oscillate back and forth over
a short distance.
Effect of Condenser. — As a further case, let us suppose that an
elastic partition -E is arranged in the pipe (Fig. 5), so that no water
can flow through or around it. If a pump P, or a piston, acts steadily,
the water moves a short distance until the partition is stretched
enough to exert a back pressure on the water equal to the pressure of
the pump, and then the movement of the water as a whole ceases.
If, on the contrary, a reciprocating motion is given to the water by P,
the water moves back and forth, stretching the partition first in one
direction and then in the other, and the water surges back and forth
between short limits which are determined by the elasticity of the
partition. We have in this case an alternating current of water in
spite of the presence of the partition.
An electric condenser acts just like an elastic partition in a circuit.
No direct current can flow through it, but an alternating current, of
an amount depending on the nature of the condenser, can flow when
an alternating emf. acts on the circuit.
As an extreme case, we may imagine the pipe line replaced by
a long tube filled with water and the ends closed by elastic
walls (Fig. 6). Suppose an alternating pressure to be given
to the water in the tube, or even let the tube be tipped, first in one
direction and then in the other. The water will oscillate back and
forth a short distance in the tube, first stretching the wall at one end
and then the wall at the other. A small alternating flow is thus set
up, although there is not a complete circuit for the water to flow
through. Analogous to this case is that of the electrical oscillation
INTRODUCTION. 21
of an antenna. Such a flow of electricity without a complete circuit
is called a * * displacement current. " It is always necessary, in order
to produce a displacement current, that the circuit shall have elec-
trical elasticity somewhere; that is, that an electric condenser
shall be present.
The importance of the electric current lies in the fact that it is
an energy current. A current of water transports energy; so does a
current of air. It is the motion that counts, and to utilize the
energy of motion we must do something tending to stop the motion.
Any material substance, by virtue of its mass, can be made to act
as a vehicle for transporting energy from one place to another pro-
vided only it is set into motion. In the case of the electric current,
we do not need to inquire whether electricity has mass. We are
concerned, in the use of electrical apparatus, with the transforma-
tion of the energy of the current into other familiar forms of energy —
heat, light and motion. The electric current is the vehicle by
which we transmit energy from the central station to the consumer,
and we are not, for practical purposes, concerned with the method
of carrying the energy, any more than we need to inquire into the
nature of the belt by which mechanical energy is carried from one
wheel to. another, or into the chemical nature of the water which is
furnishing the power in a hydraulic plant.
The electric current itself cannot be seen, felt, smelt, heard, or
tasted. Its presence can be detected only by its effects — that is,
by what happens when it gives up some of its energy. Thus, an
electric current may give up some of its energy, and cause a.
motor to turn. Electrical energy has been given up, and mechan-
ical energy takes its place. Similarly, electric energy may dis-
appear and heat or light may appear in its place, or a chemical
effect may arise. When a person feels an electric shock, it is not
the current itself he feels, but the muscular contractions caused
by the passage of the current. The electric lamp has an effect on
the eye. We do not, however, see the electric current in the lamp,
but the effect on the eye is due to the light waves sent off by the
hot filament. The energy of the current has been changed over
into heat in the lamp. When we hear a buzzing in the telephone,
it is not the electric current we hear, but merely the vibration of
the thin diaphragm. The electric current has used some of its
energy in moving the diaphragm. The acid taste noticed when
the tongue is bridged across the poles of a dry battery is due to the
22 INTRODUCTION.
chemical decompositioii of the saliva into other compounds as a
result of the passage of the current through it.
In the next section, the electric current is studied through the
effects it produces, and in later sections it is given a more exact
and detailed treatment.
CHAPTER 1.
ELEMENTARY ELECTRICITY.
A. Electric Current.
3. Effects of Electric Current. — Electricity may be stored in an
apparatus called a condenser (see Sec. 30) as air is stored under
pressure in a tank, and certain characteristic effects accompany
this condition. However, the most practical applications of elec-
tricity follow from the movement of eleotric charges — ^that is, elec-
tric current. Quantity of electricity is of importance in connection
with such subjects as electrons (Sec. 6) and capacitance.
A wire in which an electric current is flowing usually looks
exactly like a wire without current. Our senses are not directly
impressed by the phenomena of electricity, and hence it is neces-
sary to depend upon certain effects which are associated with the
flow of current through a conductor when it is desired to determine
whether or not a current exists. Some of these effects are as follows:
(a) If a straight wire is brought near a small magnet, such as a
compass needle, which is so placed that the axis about which it
turns is parallel to the axis of the wire (Fig. 7) then the needle is
deflected a certain amount and tends to become tangent to a circle
about the wire. It then remains in the new position as long as the
current does not vary.
(6) A wire with a current passing through it will be at a higher
temperature than the same wire before the current flows. This
can be readily detected by a sensitive thermometer, and under
some conditions, as in an ordinary incandescent lamp, the rise of
temperature is so great as to cause the filament to glow.
(c) If the wire through which the current is flowing is cut, and
if the separated ends are attached respectively to two metallic
plates immersed in a solution of some substance like copper sulphate,
there will be a chemical change in the solution accompanied by a
deposition of the metal copper on one of the plates.
The attention of the student should be fixed upon these effects
of the current, rather than upon the current itself. It is in terms
23
24
RADIO COMMUNICATION.
of these effects that electric currents are detected, measured and
applied. Thus the magnetic effect is the basis of dynamo-electric
machinery and radio communication; the heating effect makes
possible electric cooking and electric lighting; and the chemical
effect is the basis of electroplating. All three effects are utilized
in making electric measurements.
It must be kept in mind that such expressions as "flow" and
"current," and many other electrical terms are merely survivors
from an earlier day when electricity was supposed to be a fluid,
which actually flowed. Such terms are, however, helpful in
forming mental pictures of the real phenomena of electricity.
•'•p^ ^
strai^f Wire.
Current flo
id ^b0ut&
wir\^ down.
Md^eti'c
Current
fia.
#
Woo
ibod 5crew
iieU Aba\)\ A atnii^t wine
#
Memory ryfe -f^r diredian of <:urrsntdifv4
lines of jardo
Attention must always be centered on the facts and effects which
these terms represent and the words or phrases themselves must
not be taken too literally.^
4. Magnitude and direction of current. — By means of the mag-
netic effect it is readily shown that electric current has direction.
If the wire in Fig. 7 be withdrawn from the plate, 0, and reinserted
in the opposite direction, the compass needle will indicate a direc-
tion (Fig. 8) nearly opposite to that of its original position. The
same result is secured by interchanging the wires at the poles of
the battery.
1 Read Franklin and MacNutt, General Physics, p. 238.
RADIO COMMUNICATION. 25
The direction of flow of electric current is in any event a matter
of arbitrary definition, and in practice the student will usually
determine the direction by means of an instrument with its terminate
marked + and — . It is assumed that current enters the instrument
at the 4- terminal and leaves it at the — terminal.
The magnetic effect may also be used in specifying the direction
of the current. See Sec. 40. Again referring to Fig. 7, it is seen
that as the current flows down through the plane, the compass
needle, at every point in the plane, tends to set itself tangent to
one of the concentric circles about the wire. The north seeking, or
north pointing pole of the needle will point in a clockwise direction
around the current as the observer looks along the conductor in the
direction of the current. Other useful rules for remembering the
same relative directions are as follows:
(fi) Grasp the wire with the right hand, and with the thumb
extended along the wire in the direction of the current. The curved
finger tips will then indicate the direction of the magnetic effect,
Fig. 10.
(6) Imagine a wood screw being advanced into a block in the direc-
tion of the current, Fig. 9. The direction of its rotation then
indicates the direction of the magnetic field around the wire or
conductor.
The student should assure himself of complete familiarity with
one of these rules by considerable practice with a small compass
and a simple electric circuit.
5. Measurement of Electric Current and Quantity of Electricity. —
All three of the simple ways by which electric current may be
detected (see Sec. 3) provide means of current measurement. The
magnetic effect of the current may be used by mounting a wire and
a magnet in such positions that when a current flows in the wire
either the magnet or the wire moves. The heating effect of the
current is utilized in hot wire instruments (Sec. 49), where the
increase in length of the heated wire is utilized to move a pointer
over a dial. These principles are used in a great variety of instru-
ments for the measurement of current. The amount of current is
read from the scale or dial of the instrument. The scale is usually
graduated at the time when the instrument is standardized, in a
unit * called the * 'ampere. ' * The instruments are called ' 'ammeters
9>
1 See Appendix 2 on "Units," p. 356.
26 RADIO COMMUNICATION.
The ampere is a unit the magnitude of which has been defined
by international agreement. In its definition the third effect of
the electric current, described above, is made use of. The mass of
a metal which is deposited out of a solution by an electric current
depends on the product of the strength of the current by the time
it is allowed to flow. Thus a certain current flowing for 100 seconds
is found, experimentally, to be able to deposit as much of a metal as
a current 100 times as great passing for one second, etc. Remem-
bering that the strength of the current is the rapidity of flow of
electricity, it is evident that the product of strength of current by
time of flow gives the total quantity of electricity which has passed.
The mass of a metal deposited by the current is, then, propor-
tional to the total quantity of electricity which has flowed through
the solution. Equal quantities of electricity will deposit different
masses of different metals, but the mass of any chosen metal is always
the same for the same quantity of electricity.
The ampere {properly called the international ampere) is that un-
varying current whichy when passed through a neutral solution of silver
nitrate y will deposit silver at the rate of .001118 gram per second.
A convenient way of remembering this figure is that it is made
up of one point, two naughts, three ones, and four twos — 8. While
current could be r^^ularly measured by the process used in estab-
lishing this unit this is not done in actual practice. The measuring
instruments used in actual measurements are, however, standardized
more or less directly in terms of the unit thus defined.
6. Electrons. — When electric current flows in a conductor there
is a flow of extremely small particles of electricity, called electrons.
The study of these particles is important not only in connection
with current flow, but also in light and heat and chemistry. The
reason for this is that all matter contains them. Matter of all kinds
is made up of atoms, which are extremely small portions of matter
(a drop of water contains billions of them). The atoms contain
electrons which consist of negative electricity. The electrons are
all alike, and are in turn much smaller than the atoms. Besides
containing electrons, each atom also contains a certain amount of
positive electricity. Normally the positive and negative electricity
are just equal. However, some of the electrons are not held so
firmly to the atom but what they can escape when the atom^is
violently jarred. When an electron leaves an atom, there is then
less negative electricity than positive in the atom; in this condition
RADIO COMMUNICATION. 27
the atom is said to be positively charged. When on the other hand
an atom takes on one or more extra electrons, it is said to be nega-
tively charged.
The atoms in matter are constantly in motion, and when they
strike against one another an electron is sometimes removed from
an atom. This electron then moves about freely between the atoms.
Heat has an effect upon this process. The higher the temperature,
the faster the atoms move and the more electrons given off. If a
hot body is placed in a vacuum, the electrons thus given off travel
from the hot body out into the surrounding space. This sort of a
motion of electrons is made use of in the vacuum tube, which is
the subject of Chapter 8 of this book. The motion of the electrons
inside a wire or other conductor is the basis of electric current flow.
This is briefly discussed, with the various important properties of
electrons, in Circular No. 74 of the Bureau of Standards, page 8,
(This circular will hereafter be referred to as C. 74.)
B. Resistance and Resistivity.
7. Resistance and Conductance. — ^The flow of current through a
circuit is opposed by a property of the circuit called its * ' resistance ' *
(symbol R), The resistance is determined by the kinds of materials
of which the circuit is made up, and also by the form (length and
cross section) of the various portions of the circuit. Provided that
the temperature is constant, the resistance is constant, not varying
with the current flowing through the circuit. This important
relation is called Ohm's law and will be discussed further in Section
14. All substances may be grouped according to their ability to
conduct electricity, and those through which current passes readily
are called ** conducting materials" or *' conductors," while those
through which current passes with difficulty are called *' insulating
materials" or *' non-conductors." However, there is no known sub-
stance which admits current without any opposition whatever,,
nor is there any known substance through which some small current
cannot be made to pass. There is no sharp distinction between the
groups, as they merge gradually one into the other. Nevertheless, it
should be kept in mind that conductors have a conducting power
which is enormously greater than the conducting power of an in-
sulator. The minute current which can be forced through an in-
sulator under certain circumstances is aptly called a *' leakage cur-
rent." An ideal insulator would be one which would allow abso-
28 RADIO COMMUNICATION.
lutely no current to flow. Examples of good conducting materials
are the metals and that class of liquid conductors called electrolytes.
Examples of insulating materials are dry gases, glass, porcelain,
hard rubber, and various waxes, resins, and oils.
A circuit which offers but little resistance to a current is said to
have good conductance. Kepresenting this by g we may write
Sr=5;ori2=- (1)
For example, a circuit having a resistance of 10 ohms will have a
conductance of 0.1 and one of 0.01 ohm will have a conductance of
100. The unit of resistance called the "ohm " is defined in terms of
a standard consisting of pure mercury, of accurately specified length,
mass and temperature.
The international ohm is the resistance offered to the flow of an unvary-
ing current by a column of mercury 106.3 centimeters high and weighing
14.4^21 grams at a temperature ofO° C.
For very small resistances, the millionth part of an ohm is used as
a unit and is called the ' ' microhm. ' * For high resistances a million
ohms is used as a unit and is called the "megohm."
The opposition to flow of current referred to above is analogous
to friction between moving water and the inner surface of the pipe
through which it flows. It is always accompanied by the pro-
duction of heat. If an unvarying current is maintained through a
conductor, this production of heat is at a constant rate. The total
heat, produced in t seconds, is found to be proportional to the
resistance of the circuit, to the square of the current and to the time,
thus
W=RIH (2)
From this it follows that /2, for a given portion of the circuit, might
be measured by the heat generated in that portion. The heat will
be measured in "joules" when the current is in amperes, the resist-
ance in ohms and the time in seconds. To find the heat in calories,
the relation W/J=Hwiil be used, where Tfis in joules and /, (4.18),
is the number of joules in one calorie. The relation given in equa-
tion (2) is sometimes called Joule's law.
8. Besistivity and Conductivity. — For a given piece of wire of
uniform cross section, its resistance is found to be proportional
directly to its length, and inversely to its cross sectional area; and
in addition the resistance depends upon the kind of material of
RADIO COM3IUNICATION. 29
which the wire is composed. These relations may be expressed in
the following equation
R=PJ (3)
where R is the measured resistance of the sample, I is the length, s
is its cross section and p is a constant, characteristic of the given
material. Solving this equation for p we have
p=R-l (4)
If a piece of material is chosen having unit cross section and unit
length, it is seen that p is equ^al to the resistance of the piece, meas-
ured between opposite faces. The factor p is called the * ' resistivity "
of the substance, and is defined as the resistance between opposite
faces of the unit cube. The ohm or the microhm is commonly used
as the unit of resistance and the centimeter as the unit of length.
Instead of expressing resistivity in these units it may also be given
in terms of ohms per foot of wire one mil (0.001 inch) in diameter, or
in ohms per meter of wire one millimeter in diameter.
Another group of resistivity units is based upon the mass of a
sample instead of its volume, for example: (a) the resistance of a
imiform piece of wire of one meter length and of one gram mass;
or (6) the resistance of a wire of one mile length and of one pound
mass. Practically, for some purposes, the mass resistivity is
preferable to the volume resistivity for the following reasons: (a)
sufficiently accurate measurements of cross section of specimens are
frequently difficult, or, for some shapes, impossible; (6) material
for conductors is usually sold by weight rather than volume, and
hence the data of greatest value are most directly given. The mass
units and volume units are readily intercon verted, provided that
the density of the material is known. If in equation (3) we substi-
tute for s the value of v/l, where v is the volume, and for v its equiva-
lent ~ , where m is the mass and d is the density, we have
a
R=pd^ (5)
The quantity pc? is called the mass resistivity of the material. The
volume resistivity may then be transformed into mass resistivity,
or vice versa, taking care that all the quantities are given in
30 RADIO C0M3IUN1CATI0N.
consistent units. As examples of resistance the following wil
be useful:
1. One ohm is the resistance of about 157 feet of number 18 copper
wire, (diameter about 1 mm., or 40 mils or 0.04 in,).
2. One thousand feet of number 10 iron wire (diameter about 2.5
mm., or 102 mils or 0.1 in.) has a resistance of about 6.5 ohms.
Tables of resistivity for various materials are given in Table 21,
C. 74.
Just as conductance is the reciprocal of resistance when con-
sidering the properties of a circuit as a whole, so " conductivity " is
the reciprocal of resistivity when considering the properties of a
given material. Its unit is the *'mho," or "reciprocal ohm."
9. Temperature Coefficient. — ^The electrical resistance of all sub-
stances is found to change more or less with any change in tem-
perature. All pure metals and most of the metallic alloys show an
increased resistance with rising temperature. Carbon and most
liquid conductors like battery solutions, show a decrease in resistance
as the temperature increases. Experiment shows that the resistance
at a temperature t can be calculated, if the resistance at zero tem-
perature (melting point of ice) has been measured. The formula is
R,=R^+R,aJ (6)
where Rq is the resistance of the sample at zero, and a^ is the change
in 1 ohm when the temperature changes ^rom zero to 1° C. The
factor ao is called the " temperature coefficient" of resistance for the
material. Solving equation (6) for ao we have
"« Rj- (^)
Equation (7) shows that oq is the value of the change in the resistance
per ohm per degree change in temperature, or it is the fractional
change of the total resistance for 1 degree change in temperature. If
the resistance of the material decreases with a rise in temperature,
then the temperature coefficient is said to be n^ative.
If a reference temperature ti is chosen, which is not zero, then the
resistance i?2, at some other temperature tj, which is higher than
ti, may be found from the resistance Ri at ti by the following
equation,
R^=R,[l+a,{t,-t,)] (8)
Calculations of this sort are simplified by the use of a table of values
of a, for various initial reference temperatures. See Table 21, C. 74.
RADIO COMMUNICATION.
31
10. Current Control. — In electrical work the need is constantly
arising for adjusting a current to a specified value. This is usually
done by varying the resistance of the circuit. Changes in the re-
sistance of a circuit can be made by means of resistors, which consist
in general of single resistance units, or groups of such units made of
suitable material. These may be variable or fixed in value. Vari-
able resistors are frequently called "resistance boxes" or "rheos-
tats,'* depending on their current carrying capacity and range.
A resistance box consists of a group of coils of wire assembled com-
pactly in a frame or box. (Figs. 11, 12, and 13.) It is so arranged
that single coils or any desired combination of such coils may be
Via
F\\^ joutftnce ben
Fia.l3>
resist*nce b«A
COnnechon in ^m^
ncftistiLncc ^M
KeaiaUnce Wirt
introduced into the circuit by manipulating the switches or plugs.
The extreme range of such a device may be from a hundredth or a
tenth of an ohm, up to 100,000 ohms. Each of its component units
is accurately standardized and marked with its resistance value . By
this means, it is possible to know precisely what resistance is intro-
duced into the circuit by the resistance box. The coils are wound
with relatively fine wire, and in such a way that they do not have
any appreciable magnetic fields about them. They are intended
solely for carrying feeble currents, usually no more than a fraction
of an ampere.
32
RADIO COMMUNICATION.
The name "rheostat" is, in general, applied to a similar device,
but with a larger current carrying capacity and a smaller range. Its
coils are usually open to the air and it may be adjusted continuously
or by steps. (Figs. 14 and 15.) The familiar groups of grids sup-
ported beneath the floor of street cars is a good example of rheostat.
The individual units are not accurately measured and marbed as
they are in the resistance box, and it is usually not necessary to know
the values of the separate steps. A frequently used resistor for large
currents is made by immersing plates in a tank of a conducting
liquid. Adjustments are made by varying the distance between
the plates. For smaller ranges, the carbon compression rheostat is
much used in laboratory work. In this type, a number of carbon
plates are brought into more or less intimate contact by a variablp
screw pressure.
Resistors of single fixed values are convenient for many purposes.
If they are carefully made and precisely measured they 'are often
Tube RhaoaUt
r\Q. 14
Field I^hee^t
FIQ. 15
called standard resistance coils. Such standards may be secured
in range from 0.00001 ohm to 100,000 ohms, and of any desired cur-
rent carrying capacity and degree of precision.
Banks of incandescent lamps in various arrangements are often
used as resistors. The resistance of such lamps is subject to large
variations in value with changes in temperature. However, when
operating under steady conditions, either hot or cold, they are
satisfactory for many purposes. Such a rheostat offers the advantage
of being readily adjustable by turning lamps off or on. It is com-
pact and there is no danger of overheating.
11. Conducting Materials. — Conducting materials, usually metals
or metallic alloys, are utilized in electric circuits with two different
purposes in view. In one case a high degree of conductivity is
RADIO COMMUNICATION. 33
required, while in the other case relatively high resistivity is de-
sired. These cases will be discussed in turn.
(a) If the conductor is transmitting energy to a distant point by
means of the electric current it is seen from equation (2) that some
energy will be wasted in the conductor in the form of heat. This
loss should be kept as small as possible, and to this end great care
is taken in choosing the size and material of the conductor. For
reasons of economy the cross section must not be too great, hence a
desirable material for conducting lines must have low resistivity
and must be abundant and relatively cheap to produce. Such a
material is copper. Where lightness is important and where in-
creased dimensions are not a disadvantage, aluminum is much used.
Steel is used where great strength is desired and where the current
is small, as in telegraph lines. For lines which must stand great
strain and at the same time be good conductors, such as radio
antennae, a stranded phosphor bronze wire is often used.
(6) On the other hand, a material which is to be used for resistor
coils should have the. following properties:
1. The resistivity should be high, so that a large resistance may
be realized without too great a bulk.
2. The resistivity should be constant, so that when a coil is once
adjusted to a given value there will be no progressive changes in
its resistance as time goes on.
3. The temperature coefficient should be small, so that changes
in temperature will not appreciably affect the resistance values.
4. The thermoelectric effect (see Sec. 15) between the chosen
substance and copper or brass should be small, so that variations in
temperature between different parts of the circuit will not cause
troublesome thermal currents.
Copper, although widely used as a conductor, has too low a resis-
tivity and too large a temperature coefficient to be useful in resistor
units. Iron likewise is neither high enough in resistivity nor con-
stant enough in its behavior, except for use in certain types of
rheostats. Many of the alloys of copper and nickel have a suffi-
ciently high resistivity, but they develop large thermal emfs. against
brass and copper, which makes them undesirable for precision
resistors. In the alloy manganin, however, a very satisfactory
resistance material is realized. It has high resistivity, and practi-
cally negligible,temperature coefficient and thermoelectric effect.
97340*— 19 3
34 RADIO COMMUNICATION.
Table 21, C. 74, gives the properties of some pure metals and
the composition and electrical properties of certain of the more
common alloys.
Wire Gauges, — Sizes of wires are specified in two general ways,
either by giving the actual diame!ter in millimeters or in mils (1 mil=
0.001 in.), or by assigning to the wire its place in an arbitrary series
of numbers called a wire gauge. Only two of these arbitrary wire
gauges are of importance in American practice, the American Wire
Gauge and the Steel Wire Gauge. To avoid confusion the name of
the gauge must always be given with the gauge number. Most steel
wire is specified in terms of the steel wire gauge. Wire used in
electrical work, such as copper, aluminum and the copper-nickel
alloys, is specified in terms of the American Wire Gauge. This
is the only gauge in which the successive sizes have a definite
mathematical relation.
It is convenient to remember that any change of three sizes of
this gauge, doubles (or halves) the resistance of a wire; a change of
six sizes doubles (or halves) the diameter, and therefore quadruples
(or divides by four) the resistance of the wires.
12. Kon-conducting or Insulating Materials. — The importance of
good conductors, in practical applications of electricity, has been
dwelt on in the preceding section. It is however equally impor-
tant to have non-conducting materials in order that electric current
may be confined to definite and limited paths. Such materials are
commonly called insulators or dielectrics. It is a famiUar fact that
electric wires are covered with layers of cotton, silk, rubber and other
non-conducting compounds, and are supported on porcelain knobs
or in clay tubes. This is done to prevent the current from escaping
along a chance side path before the desired terminal point is reached.
Strictly, there is no such thing as a perfect non-conductor. The
materials commonly used for this purpose have volume resistivities
ranging from 10,000 ohms to 10^^ ohms between opposite faces of the
unit cube. This means that 1 volt impressed across such a unit
cube by means of proper metal terndnals, would cause a current of
1 1
from to xrfr^f ampere to flow. (See Sec. 13.)
Most insulating substances show a decrease in volume resistivity
with increase in temperature. These changes are irregular and
sometimes rapid. They are not directly proportional to the changes
in temperature. Humidity is of great influence, and tends to lower
RADIO C03IMUNICATION. 35
the volume resistivity in such materials as slate, marble, bakelite
and hard fiber. Very frequently surface leakage is of greater im-
portance than volume conduction, and this surface leakage is largely
dependent upon the moisture film upon the surface. Some sub-
stances acquire a surface film of moisture more readily than others.
In any event, care must be taken to ensure that its effects are either
eliminated or allowed for.
In work involving high potential differences the property of di-
electric strength is of greater importance than volume resistivity.
If the potential difference applied between opposite sides of a sheet
of dielectric material exceeds a certain critical value, the dielectric
will break down, as though under a mechanical stress, and a spark
will pass between the terminals. In case the dielectric is a liquid
or a gas, its continuity is immediately restored after the spailc has
passed. However, in a solid dielectric the path of the spark dis-
charge is a permanent defect, and if enough energy is being supplied
from the source, a continuous ciurent will persist, which flows
along the arc or bridge of vapor formed by the first spark. "Di-
electric strength" is a property of the material which resists this
tendency to break down. It is measured in terms of volts or kilo-
volts required to pierce a given thickness of the material. Values
of dielectric strength of air are given in Chapter 5, Section 171. It
is a quantity that cannot be specified or measured very precisely,
because the results vary with (a) the character of the voltage,
whether direct or alternating, (6) the distance between the termi-
nals, (c) the time for which the voltage is applied, and (d) the shapfe
of the terminals. The presence of moisture lowers the dielectric
strength. Dry air is one of the best of the insulating substances^
but its dielectric strength is lower than that of many liquids and
solids.
In addition to the constant currents which flow through or over
insulating substances, due to the *'body leakage" and *' surface
leakage " we find two other currents which are temporary, but which
it is important not to overlook.
1. The "displacement current" which is discussed later in
Section 29. This current appears and becomes negligible in a very
short time, not more than a few thousandths of a second.
2. The "absorption current" which persists longer and is ob-
served when an emf. is applied to a plate of a dielectric by means
of electrodes as in the case of a condenser. (See Sec. 31.)
36
RADIO COMMUNICATION.
At first there is a considerable rush of current but this falls off
with the time at first rapidly, then more slowly. It may not be-
come negligible for several hours. It is due to some rearrangement
of the molecules of the substance under the stress of the applied
emf.
€. Potential Difference, Emf., and Ohm's Law.
13. The Meaning of Emf. — In Section 2, it was stated that one of
the important electrical quantities is the electromotive force, which
is the cause of the electric current. In order to fix in mind the
ideas underlying the electric circuit, it will be helpful to consider
FlQ.lfe ^,^
5.
t
FIG. 17
"mre
^sz
gSS
Tr*cK
some illustrations drawn from experiences familiar to every one.
Assume that a body of 1 pound weight is raised from the floor to a
table, through a height of 3 feet (Fig. 16). Work is done upon the
body, and the amount of work done is given by 1X3=3 ft.-lb.
The body has acquired "potential energy" by this change in its
position. That is, it is capable of falling back to the floor by itself,
and in falling back it will, when brought to rest, do an amount of
work exactly equal to that which was done in lifting it.
The difference in level between floor and table may be expressed
in either of two ways; first, ia the ordinary way, by stating directly
the vertical distance through which the body was raised; and second,
RADIO COMMUNICATION. 37
by stating the amount of work required to carry 1 lb. of matter
from the lower to the higher level. This difference in level, then,
defines a very definite difference in condition between the two posi-
tions. The higher position, considered as a point in space, has a
characteristic which distinguished it from the lower position, and
that is the amount of potential energy possessed by a body when
placed there. In other words, a body placed at this point is able,
by virtue of its position, to do a certain amount of work. If we
assume that the body has unit mass this characteristic is called the
gravitational potential of the point. The higher position is said to
have a higher potential than the lower position, and the difference
in potential, measured in terms of work, is a measure of the differ-
ence in height.
Following this illustration a little further, we may consider the
case of a simple pump, which raises water from a level Si to some
higher level S2 (Fig. 17). The water raised by the pump to the
level ;S^2 poasesses potential energy or energy of position. That is,
it is able to fall back by itself to the lower level, and in falling
back it will do an amount of work exactly equal to that which was
done in lifting it. Instead of measuring the difference in level by
the height h, as before, it may be measured in terms of the work
done in lifting 1 lb. of water from Si to S2' This difference in
level may be called the difference in potential between Si and S2-
The puirpose of the pump is to transform the energy supplied by
some steam engine or other prime mover into potential energy, with
the corresponding difference in level or pressure head. This estab-
lishes what might be called a watermotive force, which causes or
tends to cause a flow of water through a return connecting pipe.
Coming now to the electrical case, let us consider that electric
current is supplied to the motors of an electric car by means of a
generator G, Fig. 18, and two conductors, the trolley wire and the
track. Mechanical energy is being supplied to the generator by
some source of power, such as a steam engine, and is being trans-
formed into electrical energy. This transformation results in a flow
of current as indicated by the arrows, when a complete circuit is
made through the car motors. This condition is described by saying
that there is a difference of electric potential between the terminals
of the generator, or between the trolley wire and the track. It is the
purpose of any electric generator to set up this difference of potential
between its terminals, which corresponds to the difference in level
38 RADIO COMMUNICATION.
of the water in the earlier illustrations. Difference of electric poten-
tial is then a difference in electric condition which determines the
direction of flow of electricity from one point to another.
Just as height of water column or difference in level may be
regarded as establishing a pressure or watermotive force, which in
turn causes a flow of water when the valves in the pipe are open, so
the electric potential difference may be regarded as establishing an
electromotive force which causes a flow of electricity when a con-
ducting path is provided. Electromotive force may be defined as
that which causes or tends to cause an electric current.
The unit of electromotive force is the volt. It is that emf which will
cause a current of 1 ampere to flow through a resistance of 1 ohm.
The relation between electromotive force, current, and resistance
is called Ohm's law. This law is discussed further in the next
section.
The potential difference between two points may be measured in
terms of the work done in conveying a unit quantity of electricity
from one point to the other. In general
W
^ Q
where ^ is in volts, TFis in joules and Q is in coulombs. (See Appen-
dix 2, Units. ) In practice, however, it is measured by direct applica-
tion of an instrument called a "voltmeter." (See Sec. 50.)
14. Ohm's Law. — If the pressure upon a pipe line is increased,
the flow of water through it in gallons per minute is increased. Ohm
found that an increase in the emf. applied to a given conductor
caused a strictly proportional increase in the current. Doubling
the emf. causes exactly twice as great a current as before, trebling
the emf., three times as great a current, etc. This means that for a
given conductor the ratio of emf. to current is a constant, and this
constant has been called the resistance of the conductor. This
important relation is known as Ohm's law, and may be written:
j=R (9)
or. in the alternative forms,
E^RT (10>
and
/=f (11)
RADIO COMMUNICATION.
39
Ohm's law derives its great importance from the fact that it applies
to each separate portion of an electric circuit and also to the circuit
as a whole.
Case I. Ohm's Lnwfor a Portion of a Circuit, — Assume some part of
a complete circuit, i?, Fig. 19, which is held at a constant tempera-
ture, and has no battery or other source of emf. between the points
A and B. If ciurent from an outside source is then caused to flow
through R, and correct instruments are used for measuring current
and voltage, respectively, the following data may be taken, showing
that i?^ has a value of 2 ohms, and that R being constant the current
is directly proportional to the voltage.
R
E
/
Ohms.
Volts.
Amperes.
2
1
h
2
1
4
2
3
8
4
10
5
Suppose two straight lines Y and OX are drawn at right angles to
each other, Fig. 20. Divide each line into units and set down the
proper numbers at regular intervals along these two lines. ^ The
niunbers on the Y axis may be used to represent values of E, and
the numbers on the OX axis to represent values of /.
At a point 1 on the E axis draw a light line parallel to the OX
axis, and from the point \ on the OX axis draw a light line parallel
to the Y axis. Where these two lines intersect make a dot. Pro-
ceed in this way for all the corresponding values of E and I in the
table above, and then connect the dots by a line. It is seen that
the ratio of .S to J is the same for every point that may be taken
on the line OP. This means that E and / are connected by a con-
stant factor and I is said to be directly proportional to E. This
process is called plotting the relation between the two quantities
E arid /. Proportionality is indicated by the straightness of the
plotted line.
Again, assume that a constant voltage E^ is applied across the
terminals of R^ Fig. 19. By some suitable means, change the
1 These lines are called axes. y is called the axis of ordinates and OX is called
the axis of abscissas. A distance measured along Oy is called an ordinate. A dis>
tance measured along OX is called an abscissa.
RADIO COMMUNICATION.
values of R through a considerable raDge. The following ai
valuea which careful observBtion might yield .
vt
Ohms.
/
12
»
Plot the values of R and / o
the curve AA ie obtained.
Also we may plot reciprocate
abscissas, against values of /
CTOBB-Bection paper, Fig. 21, and
R (values of l/R) on
of ordinatea. Fig. 22. It
ie now seen that J is proportional directly to the reciprocal of R, or
in other words, Jia inversely proportional to R. The student should
make some experiments of this sort with a resistance box, battery,
ammeter and voltmeter. He should also make a careful record of
the readings taken, and then should plot them on cross-section
paper, as suggeeted above. From such a study it will be found
RADIO COMMUNICATION. 41
(a) For a constant resistance, the current flowing is directly pro-
portional to the voltage.
(6) For a constant voltage the current is inversely proportional
to the resistance.
It is customary to speak of the current flowing "in*' a circuit; of
the resistance "of" a circuit and of the emf. "between the termi-
nals" of, or "across" any portion of a circuit.
The relation expressed in equation (10) applied to a part of a cir-
cuit is used so much practically, that the value of E^ between A and
B (Fig. 19) has been given various names. It is called (a) the RI
drop, (6) the potential drop, or (c) the fall of potential in the portion
of the circuit between A and B. If a branch circuit which contains
a current indicating instnunent, such as a voltmeter, (Fig. 19) is con-
nected between these two points, a flow of current is shown to be
taking place. The point A is at a higher electric potential than B,
and hence current will flow along the path A — Vm — B,
Case II. Ohm^s Law for a Complete Circuit. — In extending this idea
to the entire circuit, the total resistance of the circuit must be used.
This must include the internal resistance of the generator or battery,
or the sum of the resistances of all the generators^if there is more than
one. Likewise the voltage must be the resultant or algebraic sum
of all the emfs. in the circuit. Ohm's law for the complete circuit
may then be written in the form:
j_ ±E,±E,±E,± _E
i2i+72,+i?3+ R ^^-)
In this equation R must be the sum of all the resistances in circuit,
including the resistances of all the batteries or generators. In the
the same way E must be the sum of all the emfs. , each with its proper
sign. For example, there might be a number of batteries in series
(see Sec. 24) and one or more of these might be connected into the
circuit with the poles reversed. These emfs. would have to be sub-
tracted, hence the negative sign for the terms in the numerator.
Another way of stating this general law when all parts of the cir-
cuit are in series is to equate the total emf. impressed on the circuit
to the sum of the RI drops in every separate portion of the circuit,
E=:RI^RJ^RoJ+R^I+ (13)
Ohm's law is to be regarded as an experimental truth, which has
been established by countless tests for all metals and conducting
42 RADIO COM3IUNICATION.
liquids. For gases at low pressures it does not hold, nor does it
apply to certain non-conductors, such as insulating oils, rubber, and
paraffin.
15. Sources of Kmf. — There are a number of way^ in which elec-
tric energy can be derived from other forms of energy. Each one of
these energy transformations sets up a condition which causes current
to flow, that is, it produces an emf. The principal sources of emf .
will be discussed briefly in the following sections.
Static or Frictional Electricity. — ^When a piece of hard rubber is
brought into close contact with a piece of cat's fur and then separated
from it, two things may be noticed:
1. The bodies have both acquired new properties, and are said to
be electrified.
2. A force is required to separate the bodies and work is done if
they are moved apart.
Both bodies now have the power of attracting light bits of chaff
or tissue paper. The rubber is said to have a negative charge and
the fur, a positive charge. These charges exist in equal amounts
and taken together they neutralize each other. An uncharged
body is said to be neutral. When these charges are at rest upon con-
ductors they are called electrostatic charges. Electric charges may
be communicated to small light bodies, like pith balls, and if these
are suspended from silk threads the effects and properties of the
charges may be studied in terms of the motions and behavior of the
pith balls. Two pith balls charged oppositely are found to attract
each other, and two with like charges to repel each other. The
force between them in either case is proportional to the product of
the charges and inversely proportional to the square of the distance
between them. The force is also proportional directly to the value
of the dielectric constant. (See Sec. 31.)
Electrostatic forces are ordinarily very small. There are many
substances other than the two mentioned, which become charged by
friction with other materials. As glass is such a substance, the glass
face of an instrument should never be wiped with a cloth just pre-
vious to use, as it thus may accidentally become charged to such
an extent as to affect the light needle below it and cause a consid.
erable error in its reading. In case this has happened, breathing
upon the glass or wiping it with a moist cloth will remove the charge.
If two bodies carrying opposite charges are connected by a con-
ductor, a momentary flow of current takes place, and the two bodies
RADIO COMMUNICATION. 43
come to the same electrical condition. If the original charges
were equal, both bodies are dischai^ged.
Electrostatic experiments can be best performed on a cold day
when the air is dry.*
Batteries. — ^When two plates of different substances, such as two
metals, or a metal and carbon, are placed in a water solution of certain
salts or acids, there is found to be a difference of potential between
them. If the exposed parts of the plates, called the electrodes,
are connected by a conductor, current will flow. The following
list contains the names of some of the substances which are used
as battery electrodes. The order of the arrangement is such that
when any two are taken, current will flow through the wire from the
one appearing higher in the list to the one farther down:
+ Carbon.
Mercury.
Copper.
Iron.
Lead.
Cadmixmi.
Tin.
Zinc.
— Magnesixmi.
The salt and acid solutions used are conductors of electricity,,
but their conductivity is not so high as that of the metals. They
are called * ' electrolytes. ' '^ Some examples are solutions of sulphuric
acid, copper sulphate, potassium chloride, and sodium chloride
or common salt. Ordinary water from the service pipes contains
enough dissolved substance so that it conducts electricity to &
slight extent. With any two materials of the table dipped in one
of the solutions mentioned, there will be produced an emf. and a
1 For further study of electrostatic phenomena the student is referred to Crew^
General Physics, Chap. IX; Franklin and MacNutt, General Physics, Chap. XV;
Starling, Electricity and Magnetism, V; S. P. Thompson, Elementary Lessons in
Electricity and Magnetism, Index; W. H. Timbie, Elements of Electricity, Chap.
XI; Watson, A Textbook of Physics, pp. ft33-680.
* Not only do electrolytes conduct electricity, but when a current is passed through
them, the molecules of the acid or of the salt are decomposed or broken up. The
metallic part of the molecule, or its hydrogen, always travels toward the terminal
from which the current leaves the solution, and is deposited there. This is the
basis of electroplating processes, and it is in terms of such a process that the ampere
was defined. (See Sec. 5.)
44
RADIO COMMUNICATION.
resulting flow of current. The farther apart the selected materials
stand in the list the greater will be the effect produced.
This arrangement for producing a current is called a "voltaic
cell.'* Several types of this cell will be described in sections 17
to 19.
Thermoelectricity. — ^Assume pieces of two different metals CJ and
C^/, Fig. 23, soldered together at the point /. The other ends are
connected by a copper wire through the galvanometer g. If the
point of contact, or junction /, is heated to a temperature above that
of C and C\ there will be a
flow of current through the
galvanometer. This is com-
monly explained by saying
that at the junction /, heat
energy is transformed into
electrical energy, and this
junction is regarded as the
seat of an emf . In case the
temperature of / is lower
than that of CC\ the direc-
tion of the current will be
reversed . In the following
table some common metals
are so arranged that when any two of them are chosen for the cir-
cuit, current flows across the heated junction from any one to one
standing lower in the list.
Bismuth.
Platinum.
Copper.
Lead.
Silver.
Antimony.
The presence at the junction of an intermediate metal or alloy
like solder, will not affect the value of the emf. developed, because
whatever effect is developed at one point of contact with the solder,
is annulled at the other. Of the piu'e metals, a thermocouple made
of bismuth and antimony gives the greatest thermoelectromotive
force for a given difference in temperature. However, certain alloys
are frequently used for one or both of the materials. The purity and
RADIO COMMUNICATION. 45
physical state of these materials is an important factor in securing
uniformity of results. A thermoelement or thermocouple may be
calibrated with a given galvanometer; that is, a curve may be
plotted coordinating microvolts and temperatures. It then becomes
a valuable device for measuring temperatures, especially where
other forms of thermometer cannot be used. For the range from
liquid air temperatures, —190° C, to 200° or 300° C, copper-advance
or iron-advance thermocouples are often used. For high tempera-
tures, upward of 1700° C, a thermocouple of platinum and a plati-
num-rhodium alloy is used.
• Thermocouples find application in radio measurements in hot
wire ammeters. See Section 59.
Induced Emf. — Electromotive force may be set up in a circuit by
the expenditure, of mechanical work in pushing wire conductors
across magnetic lines of force. See Section 45. Also when electric
current in any circuit is caused to vary, an emf. which is the result
of this variation arises in a nearby circuit. The principles which
apply to these cases are fully stated in Sections 45 and 47. The
development of machinery based upon these principles is the sub-
ject of Chapter 2.
The RI Drop. — When for some purpose a voltage is desired which
is less than that of the available battery or generator, or one which
can be readily adjusted to any desired value, it is often convenient
to take advantage of the RI drop across a given resistance, as de-
scribed in Section 14, and to arrange a circuit as in Fig. 24. The
current from the battery which flows through the resistance ah can
be adjusted to any desired value by properly choosing the value of
ah.
Since the voltage drop along ah is directly proportional to the
resistance r, any desired fraction, — E^ may be obtained by setting
the contact c at such a point that the resistance ac is equal to — r. This
follows from equation (10) where it is seen that the emf. across any
resistance is directly proportional to that resistance so long as the
ciurent remains constant. This is nearly enough true for practical
purposes if it be assumed that the resistance of ah is relatively large
as compared to the internal resistance of the battery. The resist-
ance ah may be in the form of a resistance box with a travelling
contact at c, or it may be a uniform homogenous wire, with an
adjustable contact point at c. Such a device for subdividing a
. (
46
RADIO COMMUNICATION.
voltage is called a ''voltage divider," and has often been erroneous-
ly called a potentiometer.
Standard of Electrornotive Force. — The emfs. due to the ordinary
battery cells are usually between 1 and 2 volts. A certain type of
cell has been selected by international agreement as a standard of
emf. The type now most used is called the Weston standard cell,
because it was first suggested by Weston. It is also called the ' 'cad-
mium cell," because cadmium is used as the negative electrode.
This cell is made from carefully selected chemicals of great purity,
and when used under controlled temperature conditions its voltage
can be depended upon to remain constant within a few parts in
H
i-
^^A/y^AVVVV\AAAAA^A^^^AAAAAA/^ -■
Line
p"g
Kg).
Fio. ts
-HI .
AAAAAAA^A f'^-^^
100,000. At 20° C, its emf. is 1.0183. The value of the volt is
maintained by reference to similar cells kept in the national
standardizing laboratories.
16. Internal Voltage Drop and Line Drop. — Reference to equation
(12), page 41, will show that the voltage or emf. of the generator,
whether battery or dynamo, must always be thought of as being
expended in three parts, as follows:
1. That part which sends current through the generator itself,
called the "internal drop."
2. That part which sends current through the line, called the
*'line drop."
RADIO COMMUNICATION. 47
3. That part which sends current through the tenninal apparatus,
such as lamps, motors, or heating coils. This is the useful part of
the emf. , the first two being wasted so far as useful work is concerned.
This division of the generated emf. is illustrated in Fig. 25. Since
part 3 is the part which is applied in the external circuit, it is clear that
the generator must always supply a higher voltage than is needed
at the terminals in order to take care of parts 1 and 2. The above
facts may be again stated in the form
Total emf.=drop in generator-fdrop in line+useful drop in load.
Voltage Drop in Battery or Generator. — Assume a circuit as shown
in Fig. 26. As long as the key K is open, the battery is not sending
current through the circuit R. A high resistance voltmeter Vm
gives a reading E which is the full open circuit voltage of the cell.
The voltmeter current is so small that the cell may be regarded as
supplying no current through it. If, without removing the volt-
meter, the key K is closed , a current / flows through the external
circuit R, and the voltmeter reading is seen to drop back to some
value E^ which is less than E. As R is made smaller the value
of E^ continues to decrease, until when i2=0, that is when the poles
of the cell are short-circuited, the voltmeter shows no deflection
whatever. The voltmeter indicates at any instance the then existing
value of the voltage at the cell terminals and this may vary from the
open circuit voltage or emf. E, to zero, depending upon the external
circuit condition. For any value of R the current flowing is given
by the equation
where r is the internal resistance of the cell, or
E=RI-\-rI (15)
Thus the emf. E, is equal to the sum of the potential drop in the cell
and the RI drop in the external circuit. Denoting RI by E\ we
may write equation (15) in the form
E'=E-rI (16)
The quantity E^ is called the "terminal potential difference," or
the "terminal voltage" of the cell, and it is always less than the full
emf. by the RI drop in the cell itself. It may be defined as the
useful part of the emf., or that part which is available for sending
current through the external circuit.
48 RADIO COMMUNICATION.
The emf . E is determined once for all by the choice of materials
used in the cell, and it can not be in any way altered after the cell
is once chosen. The terminal voltage however can be varied
through all possible values from E to zero. Anything that may be
done to lessen the internal resistance of the battery, such as putting
several cells in parallel (see Sec. 24), will lower the RI drop and
correspondingly increase the terminal voltage E\ After the RI
drop has been subtracted from the emf. E, the balance is the terminal
voltage, or that part of the emf. which is available for work in the
external circuit. The current drawn from the battery must be
regarded as flowing through the entire circuit. As this value of I
increases, the internal voltage drop in the battery increases, and a
correspondingly smaller fraction of the total emf. is available for
the external circuit.
What has been said here of a cell is equally true of any other
form of generator.
Voltage Drop in the Line. — Suppose that a d.c. generator, capable
of supplying 115 volts at the outgoing wires of a powerhouse is
furnishing current to a distant building for lighting lamps which
require 110 volts. Suppose that the line resistance is 0.1 ohm and
that the lamps require 50 amp. of current. There is then a line
drop of 5 volts, and the available voltage at the generator is just
right to operate the lamps at their rated voltage. Suppose, how-
ever, that other apparatus near the lamps, say, the motor of an
electric elevator, is put in operation, and that this requires 100
amp. of current. The line drop is then increased by 10 volts,
or 15 volts in all, and the voltage available at the distant end of the
line has fallen to 100 volts. This is not enough to maintain the
lamps at full brightness and they are dimmed perceptibly every
time the elevator is operated. To correct this difficulty, a new line
of lower resistance must replace the old one; that is, the line drop
must be decreased, so that for the maximum current demand the
lamps will not fall below 110 volts.*
Another example of the line drop is seen in the dimming of the
lights of a trolley car when the car is starting. The resistance of the
trolley wire is kept low by using a large cross section of copper, and
the track resistance is kept as low as possible by careful bonding at
^Problem.— Assuming that the distance from powerhouse to lamps is \ mile, cal-
culate the resistance of the line which is necessary to maintain the lamp voltage
at 110 volts. Find also the size of copper wire which should be used for this line.
RADIO COMMUNICATION. 49
the rail joints. However, a few defective joints raises the track
resistance and increases the line drop to such a degree that the
necessary lamp voltage cannot be maintained when the car starts.
D. Batteries.
17. Kinds of Cells. — An electric battery is made up of a group of
cells so arranged as to produce a greater effect than one alone. The
term "battery" is sometimes incorrectly used to mean one such
cell. We have seen that the cell is a device for converting chemical
energy into electrical energy. There are two principal types of
cells. One, in which the action can only be renewed by putting in
new chemicals or parts, is called a "primary" cell. In the other
type of cell the necessary chemicals can be renewed by a charging
process; i. e., sending current through the cell in a direction oppo-
site to that which the cell itself produces. Such cells are called
"secondary" or "storage" cells. They can be used over and over
again without putting in fresh chemicals. A group of these is
commonly called a storage battery. These will be discussed more
fully in Section 21.
18. Simple Primary Cell. — If a plate of pure zinc and a plate of
copper, not in contact with each other, are immersed in dilute
sulphuric acid, no chemical action takes place. When the plates
are connected by a wire or other conductor outside of the liquid a
current flows in the wire and a chemical action occurs in the cell.
The sulphuric acid attacks the zinc, forming zinc sulphate, and the
hydrogen liberated from the acid appears at the copper plate. The
direction of the current flow is from the copper plate out around the
metallic circuit to the zinc plate and then back through the acid to
the copper plate. The direction of this current in the external
circuit is arbitrarily said to be from the copper or positive plate to
the zinc or negative plate. In diagrams, such as Fig. 27, p. 50, the
positive plate is indicated by a plus sign (-f), and the negative
plate is indicated by a negative sign (— ). If an ammeter or volt-
meter is connected into the circuit its positive terminal is connected
to the positive plate of the cell.
Every primary cell has two plates, called "electrodes" or poles,
and a liquid called the "electrolyte." The electrodes are metals
or carbon, and the two electrodes cannot be the same substance.
Among the commonly used electrolytes are solutions of sulphuric
acid, copper sulphate, ammonium chloride, and other chlorides.
97340°— 19 4
50
RADIO COMMUNICATION.
The voltage given by the usual cells is between 1 and 2 volts per
cell. The voltage of a cell depends mainly upon the pair of sub-
stances used as electrodes, and is affected somewhat also by the
electrolyte. Thus, a great many different electrolytes are used to
make up cells with copper and zinc as electrodes, but all give close
to 1 volt per cell. This fact is often very useful when a certain
voltage is wanted and no regular source is available. By taking
two different metals and placing them in any acid which does not
attack them violently, or even in water, an emergency source of
voltage can often be secured.
Local Action, — ^When a piece of pure zinc is placed in a solution of
sulphuric acid, no action is observed to take place and no hydr(>gen
is evolved. When the plate of zinc contains impurities, however,
such as particles of iron or carbon, a considerable action with the
1
^^■f:^
:5imi)le VolUic Cell
f\C.TX
Orcuit
not©
evolution of hydrogen is noticed as soon as the zinc is put into the
acid. The reason for this is that each particle of a foreign substance
in the surface of the zinc acts with a neighboring particle of zinc as a
voltaic cell, and the effect is that of a number of tiny cells, all
exhausting themselves in producing local currents which are purely
wasteful. This sort of local action in the ordinary cell contributes
nothing to the useful energy output of the cell.
Polarization, — The current given by the simple cell described
above does not remain constant, but begins to diminish soon after
the circuit is closed. The hydrogen which is liberated from the acid,
when current flows, accumulates in the form of small bubbles on
the copper plate. It thus diminishes the area of contact of the liqmd
with the copper, and so increases the resistance in the cell. The
presence of the hydrogen furthermore diminishes the voltage gener-
RADIO COMMUNICATION. 51
ated in the cell. Both the reduction of the generated voltage and
the increase of resistance decrease the current given by the cell.
This behavior caused by the hydrogen is called polarization. The
effect disappears a while after the circuit is opened, by gradual dif-
fusion of the hydrogen away from the copper surface. Polarization
may be prevented by placing some substance around the copper
plate to remove the hydrogen or prevent its formation. It is for this
reason that primary cells contain a chemical substance called the
"depolarizer" in addition to the electrolyte.
The action of the depolarizer is limited to the positive plate,
and it is kept from contact with the negative plate in various
ways. In the "gravity cell, " one of the forms of Daniell cell men-
tioned in the table just below, the depolarizer is copper sulphate
solution, which is kept separate from the electrolyte by the action of
gravity. Being denser than the electrolyte, it remains at the bottom
of the vessel. The copper is placed at the bottom, in the depolarizer,
and the zinc is placed at the top in the electrolyte. Another method
of keeping the depolarizer away from the negative electrode is by
the use of a porous cup or partition, through which the current can
pass, but the liquids can diffuse only with difficulty. This may be
of paper, cloth, or porous porcelain.
Characteristics of Good Primary Cells. — For best results a battery
cell is usually desired which has as large an emf. as possible. This
depends upon what materials are chosen for the plates, but not at
all upon their size or arrangement. If a large current output is
desired, the internal resistance of the cell must be low. This de-
pends upon the electrolyte chosen, and also upon the size and
arrangement of the plates. Large plates, close together, set in an
electrolyte of low volume resistivity are the conditions necessary
for low internal resistance. Constant emf. is only possible if the cell
is free from polarization. Economy in operation depends on low
first cost of materials and freedom from waste due to local action.
The operation of the battery should not yield disagreeable or poi-
sonous fumes. Dry cells, such as are described below, have all of
the desirable characteristics here mentioned except that they do
polarize.
19. Types of Primary Cells.
Closed Circuit Cells. — Cells which are used with the electrical
circuit closed for fairly long periods of time must be particularly
free from polarization; i. e., the cell must have an effective depolar-
52
RADIO COMMUN IC ATION .
izer around the positive plate to prevent hydrogen from collecting
on it. The make-up, generated voltage and approximate resistance
of typical cells are given in the following table.
Name.
Positive
elec-
trode.
Nega-
tive
elec-
trode.
Electrolyte.
Depolarizer.
Volts.
Inter-
nal re-
sist-
ancG,
ohms.
Darnell
Copper.
Carbon.
Copper.
Silver..
Zinc.
Zinc.
Zinc.
Zinc.
Sulphuric acid.
Sulphuric acid.
Caustic potash.
Ammonium
chloride.
Copper sul-
phate.
Chromium pe-
roxide.
Copper oxide...
Silver chloride .
1.1
2.0
0.8
1.0
1
Chromic acid
Edison-Lalande .
Silver chloride...
0.2
0.03
2
The silver chloride cell is classed as a dry cell, being made in
such a way that the electrolyte cannot spill. This cell will last a
much longer time than the more common kind of dry cell described
below.
Cells for Intermittent Service. — For service such as ringing door
bells, operating telephone buzzers, and ignition devices, a primary
cell may be used which does not have a powerful depolarizer. The
cell can recuperate from polarization during the intervals of rest
with the aid of only a slow acting depolarizer. The cell universally
used for such service is the sal ammoniac cell, having carbon as the
positive and zinc as the negative electrode, ammonium chloride
(sal ammoniac) as the electrolyte, and manganese dioxide as the
depolarizer. The voltage generated is about 1.5 volts.
20. Dry Cells. — ^The sal ammoniac cell is now used almost uni-
versally in the form of the so-called dry cell. The solution of sal
ammoniac is contained in an absorbent material and the cell is
thoroughly sealed, so that spilling is impossible.
The zinc serves as the container for the cell, being a can made of
sheet zinc about 0.045 cm. (0.018 in.) thick. The positive electrode
is a large rod of carbon in the center of the cell, and this is surrounded
by a mixture of manganese dioxide and carbon. This mixture
saturated with the sal ammoniac solution, is bulky and occupies
most of the interior of the cell. The electrolyte, sal ammoniac
solution, is contained partly in the mass of depolarizing mixture and
partly in the porous separator that is placed between the zinc and the
depolarizer. The separator is usually a thick pulpboard in large
RADIO COMMUNICATION. 53
American cells. In small cells and nearly all European cells it is a
cloth bag, spaced in from the zinc so that it is surrounded by some of
the electrolyte in the form of a paste.
The standard dry cell, called **No. 6," is 15 cm. (6 in.) high by
6.5 cm. (2.5 in.) in diameter and weighs about 900 grams (2 lb.).
There are two principal classes of these cells — ^ignition cells for heavy
service and telephone cells for light and intermittent service. There
is also an intermediate cell for general service, having characteristics
between these two. The ignition cells deliver an instantaneous
current of about 30 amp. when short circuited, provided they are
new and little used. They lose their energy and become useless in
about six months. The telephone cells give about 20 amp. on a
momentary short circuit. They last longer than the cells made for
heavy service, the usual life being about a year.
Miniature dry cells, used for flash lights and for plate batteries for
low power vacuiun tubes, are made in sizes varying from 4 to 10 cm .
in height, weighing from 14 to 100 grams. They maintain theii*
effectiveness only a few months.
The voltage generated in an unused dry cell is from 1.5 to 1.65
volts. An emf. lower than 1.45 volts in a new cell indicates dete-
rioration or defect. However, when a current is being drawn from
a cell, the voltage at its terminals is less because part of the generated
voltage is used in overcoming the internal resistance of the cell.
(See Sec. 16.)
The standard size No. 6 dry cells give a total of about 25 watt-
hours ,of energy. The amount delivered increases somewhat with
increasing temperatures. The higher the temperature, however,
the faster does the cell deteriorate when not in use. It is usually
best therefore to keep dry cells at a temperature below 25° C.^
The dry battery is chiefly useful for supplying (a) relatively large
current for a brief instant or (6) very small current for a long time.
Owing to its rapid polarization, the dry cell is not able to deliver a
steady current for a long time in service, such as operating lamps or
motors. The storage battery is much better adapted to this kind of
service.
21. Storage Cells.^ — ^The essential difference between the primary
cell previously described and the secondary or storage cell is in the
1 For further infonnation on dry cells, see Circular of the Bureau of Standards No.
79, Dry Cells, 1918; Trans. Amer. Electrochem. Soc., 21, p. 275, 1912; Electrician, 69,
p. f), 1912; 71, p. 481, 1913.
2 See also S. C. nadio Pamphlet No. 8.
54 RADIO COMMUNICATION.
manner of renewing the active material of the plates. When the
primary cell is exhausted, it is renewed by renewing the electrolyte
and removing the worn out zinc plate and putting a fresh one in
its place. Dry cells cannot be so renewed. In the storage battery,
however, the necessary chemical condition of the plates is restored
by the action of a current from an outside source. The direction of
this current is opposite to that of the current supplied by the cell.
While the cell is giving out current, it is said to be discharging.
While it is receiving current from some outside source, it is said to
be chai^ging. In Fig. 28, p. 50, is shown a typicol circuit for charging
storage cells. The dynamo D is connected through the ammeter and
rheostat R to the battery, so that the positive pole of the dynamo is
connected to the positive pole of the battery, thus sending the
charging current against the emf. of the battery. This is very
important. A mistake in connection may cause permanent injury
to the battery. Storage batteries in general have low internal
resistances, and hence they will yield relatively large currents.
Although this is an advantage, there is also the danger of excessive
currents in case of an accidental short circuit. Voltage changes
throughout the period of discharge are small, and so fairly constant
currents can be maintained. There are two types of storage cell
in common use: (a) the lead plate, acid electrolyte cell; (6) the nickel,
iron plate, alkaline electrolyte cell. Each of these will be described
in the following sections.
The Lead Plate, Add Electrolyte Cell.— In this type of cell (Fig. 29)
the plates are made of lead, and contain many apertures, so that
either plate is sometimes called a ' ' grid. " Into these holes in the
plate there is forced, by heavy pressure, a paste made by mixing
certain lead salts (red lead, Pb304 and litharge, PbO) with sulphuric
acid. If two plates thus prepared are immersed in a 20 per cent
solution of sulphuric acid, and if an electric current is passed between
them, hydrogen will accumulate at the pole from which the current
leaves the cell. This hydrogen reduces the paste to spongy lead.
In the meantime oxygen is being taken up by the other plate and
the paste is being changed here to a higher oxide (lead peroxide,
Pb02) . Thie cell now really contains a lead peroxide plate (positive)
and a spongy lead plate (negative). These materials in a solution
of sulphuric acid yield at first on open circuit an emf. of about 2.2
volts. This quickly drops to about 2 volts.
RADIO COMMUNICATION. 55
After the charging current ia cut off, if the cell is connected to a
circuit, current will flow from the cell in a direction opposite to
that of the charging current. Ab the diecharge go«e on, the voltage
gradually tails. The discharge should never be carried beyond the
point at which the open circuit voltage is r.75.
Lead plate hatterics arc usually arranged with one more negative
than positive plate. The container muat be made from a material
which the acid will not attack, such as glass or hard rubber. The
n^ative plates will be a dark gray color, and the positive plates will
be a reddish brown. The chemical changes in charge and discharge
require time, and the processes can not be unduly hastened without
injury to the cell. The manufacturer always speeifiea in amperes
the normal rate of charge or discharge, and the life and efficiency
of the cell are greatly decreased if this normal rate is disregarded.
5G
RADIO COMMUNICATION.
There is a chemical combination between the sulphuric acid and
the lead, which results in the formation of lead sulphate during the
process of discharge. This uses up acid and during this time the
density of the electrolyte grows less. WTien the cell is again charged ,
sulphuric acid is returned to the solution, and the density rises.
For testing density of battery solutions an instrument called the
"hydrometer" is used. The density of the electrolyte is the best
indication of the condition of charge or discharge of the cell. ^ The
manufacturers will furnish with the cells, information as to the
correct values of the density. The lead sulphate is grayish white
in color. It is insoluble in sulphuric acid and is a non-conductor of
•electricity. It should be entirely reconverted into lead when the
cell is charged. If the cell is repeatedly charged or discharged at
the normal current rate, the amount of lead sulphate formed will be
small and not essentially harmful. However, charging or dis-
charging at an excessive rate, or allowing the cell to remain idle in a
discharged condition, will cause an excessive deposit of lead sulphate
and the plates are then said to be "sulphated." The growth of the
crystals of the sulphate sets up stresses which tend to buckle the
plates and crowd out the active material, thus hastening disintegra-
tion. The presence of the non-conducting coating also practically
cuts off the parts of the plate thus covered and reduces the capacity
of the cell. The condition is difficult to remove, and it can only be
prevented by a careful following of the manufacturers' rules for
charging, discharging, and care. During the charge, hydrogen is
given off which forms an explosive mixture with the air. An open
flame should therefore not be brought near the cells while they are
charging.
It has been mentioned that there is a certain charge or discharge
rate specified by the manufacturer, which is most favorable for each
size and type of cell. As the size of the plates increases, larger
charge and discharge currents may be used. The capacity of a
storage battery is rated in terms of "ampere-hours," abbreviated as
"amp-hr." For example, a 40-amp-hr. cell might yield 1 amp. for
40 hours, or 10 amp. for 4 hours. However, if 5 amp. is the normal
discharge rate for this cell, it should not be charged nor discharged
at a greater rate, and 5 amp. for 8 hours represents the correct con-
ditions.
The ampere-hour capacity depends upon the size of the plates,
and upon the depth of the active material. The efficiency of either
type of storage cell is expressed in terms of ampere-hours per pound
RADIO COMMUMCATIOX. 57
■weight of cell. This ia found to oe not very different for the two
types, provided that both have been given correct care and r^ular
and careful treatment. The student should be especially warned
against directly short-circuiting a lead cell. Owing to its low
reraatance, dangerously large currents may flow, also it ia certain to
injure the cell.
The !fiekel-Iron Plate, Alkaline Electrolyte Cell. — In this type of
storage cell, Fig. 30, developed by Ediaon, the positive plate con-
sists of alternate layers of nickel hydrate and 'pure nickel flake.
t^l
«r
Cdl
^t»*
&;<k
■ tubM
-.»;«. Wu
-he
«„
Fia.3o
packed in perforated nickel plated steel tubes. Several of these
are mounted side by side in a steel frame. The negative plate
consista of iron oxide hold in a somewhat similar way. These
plates are immersed in a 20 per cent solution of caustic potash in
water, and the whole is sealed into a welded sheet steel container.
The electrolyte acts only as a carrier of oxygen between the platca
and does not form chemical compounds with the active materials.
It remains practically constant in compodlion and density throu^-
out charge and dischari^e.
58 RADIO COMMUNICATION.
The voltage while charging may rise to 1.8, WTien discharge
begins, the voltage drops at once to about 1.4, then falls gradually,
averaging about 1.2 until near the end. The discharge should not
be carried beyond the point at which the open circuit voltage is
0.9. During the charging process hydrogen gas is given off, and
since this forms an explosive mixture with air, an open flame must
never be brought near the cells. The level of the solution must be
kept above the tops of the plates. If after repeated cycles of charge
and discharge the density of the electrolyte is found to be as low as
1.16, the cells should be completely discharged, and the old electro-
lyte should be replaced by new. The care and use of Edison storage
batteries are treated in great detail in Radio Pamphlet No. 8, and
this should be consulted.
Comparison of the Two Types. — The lead cell will suffer serious
injury if not charged and discharged within its proper limits and in
a regular and careful manner. The Edison cell, however, is very
rugged and will maintain its efficiency even with considerable misuse.
A lead cell which has been fully charged will discharge in a few
weeks if left standing idle, and its capacity will be considerably
decreased. It suffers a still greater loss of capacity if allowed to
stand idle while discharged or in a partly discharged condition.
The Edison cell, on the other hand, will retain its charge over a
long period of idleness, and it may be allowed to stand idle for an
indefinite time, either wholly or partly discharged, without injury.
A complete short circuit does not injure an Edison cell, but will
seriously injure a lead cell. The Edison cell can be charged or
discharged at rates which differ greatly from the normal, without
injury. The lead cell, however, must be charged or discharged at
a rate very close to its normal rate. In the lead cell pure water
must be used to replace evaporation losses. In the Edison cell any
water may be used which is free from acids and sulphur.
Some Additional Points. — In charging, it is necessary to allow
about 2.5 vollB for each lead cell, and about 1.75 volts for each
Edison cell. If the line voltage is not sufficient to charge the entire
set of cells in series, they may be divided into groups and these
groups may be placed in parallel.
The polarity of the charging line may be tested with a voltmeter,
since the + smd — terminals are always marked on the instru-
ment. If a voltmeter is not at hand, a pair of wires from the line
may be dipped into a jar of slightly acidulated water. Gas bubbles
RADIO COMMUNICATION. 59
will fonn about one wiie (the negative) much faster than about the
other (the positive). A convenient pole testing paper may be made
by dipping strips of paper in a solution of potassium iodide in water.
If the wires are placed on such a strip of paper a few centimeters
apart, and gradually brought closer together (avoiding direct con-
tact), a brown color will appear about the + pole. Glycerin may
be added to keep the solution from drying out. To guard against
a short circuit of the terminals a lamp should be included in the
circuit.
22. Internal Resistance in Batteries. — It has been stated in
Section 16 that the open circuit voltage or emf . of any battery is
always greater than the terminal voltage measured while the cell is
delivering current. The relation between the emf. E^ the ter-
minal potential difference E\ and the internal resistance r is
given by,
E-E'=rl (17)
Moreover, the voltage that must be impressed across a storage
cell to charge it is greater than the emf. of the cell, by the voltage
drop within the cell itself. Representing charging voltage by E^^^
and with the other symbols having the same meaning as above,
FJ'-E=rI (18)
From measurements of current and open and closed circuit volt-
age, the internal resistance of the battery may be calculated. The
voltmeter used in these measurements should have a high resistance,
so that only a feeble current is drawn through its coil. A potenti-
ometer is ideal for this measurement (see Sec. 26), because it does
not draw any current from the cell at the instant of making the
measurement.
It is important to understand that the quantity r, which has been
called the internal resistance of a battery, is not a constant, but
varies with the current drawn from the cell. In some cells (e. g.,
the gravity cell) the resistance decreases with an increase of current.
In others (e. g., the dry cell) there is a rapid polarization which
tends to increase with the current output, and the back emf. of
polarization opposes the emf. of the cell and decreases the current
flow. The effect is the same as an increase in resistance of the
battery. Thus it is seen that although the factor r is an important
one, and is treated as a resistance, it is not altogether a true ohmic
resistance. A better name for it is the apparent or effective
resistance.
60 RADIO COMMUNICATION.
E. Electric Circuits.
23. Current Flow Requires a Complete Circuit. — In order to
maintain a steady flow of current, there must be a continuous con-
ducting path. This path is called the "electric circuit," and it
must extend out from the generator and back to it again. The
amount of current which flows will be larger as the resistance of the
circuit is less. If some part of the circuit is made of very high re-
sistance material, the current which is maintained is relatively small.
The complete circuit consists of two parts, (a) the external part of
the circuit, which connects the poles of the battery or dynamo out-
side; and (6) the internal part of the circuit, which is made up of
the liquid conductor of the battery or the wires in the dynamo.
When the wire of a complete circuit is cut and the ends separated, the
circuit is said to be opened or broken. If the ends of the wire are
again joined, the circuit is said to be closed.
Current Value Does not Vary Along the Circuit. — The beginning
student often has the idea that a current may start out from a source at a
given strength and then in some way become used up or dwindle away
as it goes on along the circuit. This is entirely a wrong conception
and, at the outset, it must be understood that in simple circuits for
steady currents, in which we are dealing with resistance only, the
current has the same value at whatever point in the circuit is under
consideration. As an illustration of this, consider the circuit of
Fig. 31, made up of a battery or dynamo (r, a lamp e, and a resistor R,
If the circuit is cut at a, 6, c, or at any other point, and a current-
measuring instrument (an ammeter) inserted, it will indicate the
same value of current. WTiat this value may be is determined of
course by the voltage applied and the total resistance in the circuit
but whatever its value, it is constant throughout the circuit. This
is not the case with a.c. circuits, which have distributed capacity.
(See Sec. 139.)
The same idea may be applied to a circuit such as that shown in
Fig. 32. The total current / divides at a into two parts, i^ and ij.
The sum of these components is exactly equal to /. In other words,
whatever current flows up to the point a, flows away from there.
Also the currents i^ and ij unite again at h to form the current J,
which has the same value as before.
Another important law is that the sum of the voltage drops in every
part of the circuit, including the generator, is equal to the emf. of
RADIO COMMUNICATION.
61
the generator. This has already been explained in connection with
Ohm's law, Section 16.
24. Series and Parallel Connections.
(a) Resistances in Series. — If several resistors are connected as
shown in Fig. 33, so that whatever current flows through one of them
must flow through all the others, they are said to be in * 'series."
The single equivalent resistance which may replace the entire group
without changing the value of the current, is equal to the sum of the
separate resistances. This may be proved as follows. The voltages
^
I li' ^AAAAAA/^— '
PlO.31
n . b
it
-VWNA/WNAAA/V^
ii Ki
Ir
g-fywv
\AAAA
12.3
T fVNAA/W
J L-&aJ
PlQ.3»5
Se»i.sUnc«S in Pftrwllei
FlQ.34
across JR,, JRj, JR3, etc., may be represented by E^, E2, J&3, etc. We
may then write
E,=RJ
E 2=^1^2^
Since the over-all voltage between a and h is the simi of the volt-
ages across the separate parts of the circuit, we may write for the
total voltage E,
E=E,+E2+E^=RJ-\-R2l+RJ
=IIR,+R2+R,]
=IR
where R replaces the sum of all the terms in the bracket, and is seen
to be the sum of the separate resistances.
62 RADIO COMMUNICATION.
If a number of equal resistances are connected in series, we may
write for the equivalent resistance of the group,
R=nr (19)
where n is the niunber and r is the resistance of each. When resist-
ances are connected in series^ it must be remembered that the current
is constant and the total voltage is subdivided among the various parts of
the circuit.
(b) Resistances in Parallel. — If several resistances are connected
as shown in Fig. 34, so that only a part of the<^urrent passes through
each resistance, they are said to be connected in "parallel" or
*' multiple. ' ' The voltage E between points a and b is the same over
any branch. We may then write, from equation (II),
E
. E
. E
R,
*-' R.
'' R,
Since the total current must be the sum of the three branch cur-
rents, we may add the three equations and
ii+<2+^= 1= ^W+R^+Hj
or
E=R+R+R, (20)
From equation (9) it appears that the voltage divided by the
current gives the resistance, hence the left-hand member of equation
(20) is the reciprocal of the equivalent resistance, or j.'
Hence
XV Ri XV2 R^
Two resistances in parallel occur so often in practice, that it is
well to consider this case further. Solving equation (21) for R when
there are only two component resistances we have,
R =p^ (22)
Thus, two resistances in parallel have a joint or equivalent resistance,
given by the product of the resistances divided by their sum.
RADIO COMMUNICATION.
63
When there are a laige number of single resistances, all of the same
value, in parallel, it can be shown that the equivalent resistance of
the group is given by
n
(23)
where r is the value of one resistance, and n is the number of them.
1S7
I-4t
Ei«S
f\a 35
3 t
riQ.36
WJien resistances are connected in parallel it must he remembered that the
voltage across ah^ Fig. 34y is constant, and the total current is subdi-
vided among the several branches.^
1 Exercise 1.— A current of 42 amp. flows in a circuit, Fig. 35, and divides into three
parts in the three branches, of resistance 5 ohms, 10 ohms, and 20 dims, resx>ectively.
Find the current in each branch.
Solution. — The total resistance R between a and h is given by
R 5 ^10^20
R--
' y ohms.
20.
The RI drop between a and 6 is, from equation (10), ^—^X 42 — 120 volts. The
several currents may then be calculated from Ohm's law,
. 120 „^
t5— -=-=24amp.
o
. 120 ,„
iio--jQ = 12amp.
X 120 a
Exercise 2. — A battery of internal resistance 1 ohm and 15 volts emf . is sending cur-
rent through a circuit with resistances as shown in Fig. 36. Find (1) the total current,
(2) the Rl drops across resistances 1, 4, and 5, (3) the currents through 1, 4, and 5.
64
RADIO COMMUNICATION.
(c) Batteries m Series and Parallel. — It is frequently necessary,
when using batteries, to increase the effect which a single cell can
produce. This is done by connecting the batteries in any one cf
three ways:
1. In series. Here the + side of one cell is connected to the —
side of the next one, and so on for all the cells. (Fig. 37.)
2. In parallel. In this case all the + terminals are connected
together and all the — terminals are connected together. (Fig. 38.)
3. In a combination of series and parallel groups. Several group
of cells in series may be connected in parallel. Fig. 39, or several
groups of cells in parallel may be connected in series. (Fig. 40.)
^mn
■AAAAAAAAA
Cal\* in 5erie5
-^— - R.
Ccll5 in BiPAllel
AAA/V\AAA
^^^^
AAAAAAAAA-
Three 5«ries Qrau^a in ParAllel
Fra.2>9
Three P«rtt/|«( (jtbw^ in Series
Fiq. 40
The proper combination to use in any given case is dependent upon
circumstances, but in general a series arrangement builds up voltage,
but at the same time it increases the internal resistance, while a
parallel arrangement, by decreasing the internal resistance, permits
greater current to flow. If we represent the number of cells by n,
the emf . of each cell by E, the internal resistance of one cell by r,
and the external resistance hy R, we may write Ohm's law for each
of the above cases.
^=^".1 (24)
For parallel arrangement,
RADIO COMMUNICATION. 65
For series arrangement,
F
n
For n cells in series in each group, and m such groups in parallel,
nE
If it is desired to build up a large current through R with a given
number of dry cells, especially when their internal resistance has
become relatively large through age, a series arrangement may
actually cause the internal resistance to increase faster than the
voltage. Hence, adding cells in series would result in a decrease of
current. The best use of a given number of cells to produce a stated
current, under fixed external circuit resistance, can only be deter-
mined by a* careful application of Ohm's law and the above e<|ua-
tion, having the entire circuit in mind.^
1 Exercise.— Assume a battery of two dry cells in series, each cell having an emf. of
1.5 volts and an internal resistance of 0.3 ohm. Each battery then has an emf. of 3
volts and an internal resistance of 0.6 ohm. Suppose that the external resistance in
the circuit is 0.2 ohm, and that a current of 6 amp. is to be established.
Solution.— If we try one battery, Ohm's law gives
r 3.0 _ _.
^'o:2+o:6"^-^''^°'p-
This is not enough current, so we will try two batteries in series,
^=o:2+i:2=^-28a°^p-
The current is still too small and it is seen that although the voltage has been
doubled, the current has only been increased by about 14 per cent. Trying three
batteries in series,
This is still too small and only represents an increase of 20 per cent, although the
voltage was increased threefold. Vv'e will now try an arrangement of two batteries
in parallel,
3
/= fTG"^'^ amp.
97340"— 19 5
0.2 + -2
66
RADIO COMMUNICATION.
In general the largest current from a given number of cells will be
obtained when they are so grouped that the internal resistance of
the battery is equal to the external resistance of the circuit. Bat-
teries will be connected in series when the external resistance is
large, and in parallel when the external resistance is small. In
lighting systems, with many incandescent lamps in parallel, the
lamp resistance is large compared to the line resistance, and very
nearly the full voltage is realized at the lamp socket.
25. Divided Circuits. The Shunt Law. — ^Electric circuits are
frequently arranged so that the total current is subdivided, and
made to flow through two or more branches in parallel. As shown
in Fig. 41 the total current / divides into two parts, I'l and 1*2, which
TTrT"
FIQ.41
1
-W^
M««*ur«men1' of Currant by f^tantretfwIiH-
wo.
— Hfil
jAx.
Tc7
^F^^-<V
t'
^v O^- — ^
iCx
Simple PoTentiom^tar
Fia 4Z
flow in branches r^ and r^ respectively. When so arranged, either
branch is called a Bhuni (side track or by pass) with respect to the
other. The voltage between points a and 6 is of course the same
over either of the branches. We may then write,
. E
Dividing (a) by (6) we have
. E
i,_r2
(a)
(6)
(27)
RADIO COMMUNICATION. 67
The currents in the two branches are inversely proportional to the
resistances of their respective paths. This relation is called the
*' shunt law." In other words, it means that the branch of lower
resistance carries the larger current, and the branch of higher resis-
tance carries the smaller current.
This law is of constant application in electric circuits. Suppose
that the only ammeter available is one with a scale range of 0-5
amp., and suppose that a current of 50 amp. has to be measured.
The shimt law at once suggests that we may proceed as follows.
With 50 amp. flowing in the main circuit, and with 5 amp. as the
safe current through the ammeter, a shunt s must be provided
capable of carrjong thel-est of the current or 45 amp. We may then
write from equation (27),
^^=A=1 (28)
ig 4b r
where r is the resistance of the ammeter, and 8 is the resistance of
the shunt.
Then ^—t;^
Thus to carry the required amount of current, the shunt resistance
must be one-ninth of that of the ammeter. In general it can be
proved that if J is the total current, ^
■•='[w]
(29)
The factor is called the "multiplying factor" of the shunt,
and is in the above case equal to 10.
26. The Potentiometer.^ — ^The potentiometer is primarily an
arrangement of circuits for measuring potential difference or voltage.
With the aid of certain accessories it can be used for measuring volt-
ages over all ranges, and by means of Ohm's law these measiu*ements
can be applied to the determination of a wide range of current values.
A uniform homogeneous wire, usually a meter or more in length
(Fig. 42), is stretched between binding posts on a baseboard, by the
» For proof of this equation see Swoope, Lessons in Practical Electricity, p. 146.
* The word "potentiometer" is used here in its original sense, meaning an arrange-
ment of circuits for measuring potential difference. In apparatus catalogues and in
textbooks on radio circuits the word is often inaccurately used in the sense of a
voltage divider. (See Sec. 15.)
68 RADIO COMMUNICATION.
side of a graduated scale. In series with this wire is a constant
source of current, usually a storage battery WB and a variable re-
sistor R. From equation (10) it is clear that by properly adjusting
R the voltage between A and B can be varied through wide limits.
Let us assume that (1) the end A is connected to the + side of the
battery WB^ (2) the resistance of AB is uniform from end to end,
and (3) the current through AB is constant and of such a value that
the RI drop along the wire is about 2 volts. If a standard cell, of
voltage E (about 1.0183), has its -f pole connected to the point A,
a certain point Cj can be found, such that when contact is made at
this point, the galvanometer g (see Sec. 50) will show no deflec-
tion. The absence of deflection on the galvanometer means that
the jR/dropin the wire AB up to the point Cj is just equal, and opposed
to the voltage of the standard cell. The distance Aci may be rep-
resented by c?i. Now let some other cell E^, whose voltage is to be
tested, be put in place of the standard cell E. If the voltage of this
cell does not exceed the RI drop in .45, another point Cg can be
found, for which there is no current through the galvanometer. The
distance Ac^ may be called ct^, and the RI drop over this length of
wire is just equal and opposed to the voltage of the cell E^ to be tested.
Since the RI drops along the wire are directly proportional to the
lengths, we may write
E _d,
^ E'~d\
and
This simple form of the apparatus is only capable of measuring a
voltage not much greater than that of the standard cell. If very
much higher voltages are to be measured, the high voltage is put
across the terminals of a voltage divider (Sec. 15), and some defi-
nite fraction of it is then measured against the standard cell, as
described above.
Also, any range of current can be measured by means of the poten-
tiometer. The current to be measured is passed through a standard
resistance ah of known value i?. Fig. 43. This is so chosen that the
7? J drop across it lies within the voltage range of the potentiometer.
The determination of current then consists in measuring the voltage
across ab in terms of the standard cell, and calculating the current
bv Ohm's law.
RADIO COMMUNICATION. 69
27. The Wheatstone Bridge. — ^This is a simple circuit for meas-
uring an unknown resistance in terms of a known resistance. The
method depends upon the fact that in a branched circuit, Fig. 44,
the voltage drop from a to c must be the same over the path ahc as
it is over the path ode. It then follows that for any point h which
may be chosen on the upper circuit ahc, there must be some point
d on the lower branch, such that there will be no difference of po-
tential between it and the point h. The point d can be found by
connecting one terminal of a galvanometer at b and moving the con-
tact point connected to the other terminal along the lower wire
until there is no deflection. This means that there is no current
flowing, and hence no potential difference between h and d. When
the points 6 and d have been located in this way, it can be shown ^
that there is a simple definite relation between the resistances of
d
T?-inci>le of the WNaifetor* Bri<^
Fia.45
the four arms of the circuit. (See Fig. 45.) If three of these resist-
ances are known, the fourth, r.,, can be readily calculated from the
equation
or
^2
'^1 (31)
In practice the branch adc may be made from a long, uniform and
homogeneous wire, in which case it is not necessary to know the
resistance values. If the portion abc is such a wire, the ratio of the
lengths ^1 and I2 of the segments will be the same as the ratio of the
resistances. The equation (31) may then be written
ri=n^=rj^ (32)
1 For proof of this equation see Timbie, Elements of Electricity, p. 107.
70 RADIO COMMUNICATION.
28. Heat and Power Losses. — In Section 7 it was shown that
when current flows through a resistance, heat is generated in it. It
is important to understand that this effect does not refer to heating
the resistor to a definite temperature, but rather it has to do with the
Q:eneration of heat at a definite rate. This rate may be expressed in
joules per second, calories per second, watts, or horsepower. When
the rate of supply of heat due to the electric current is just equal to
the rate of loss of heat by conduction or radiation, then the tempera-
ture becomes constant. The final temperature of any resistance coil
through which current is passing depends upon its surroundings. If
it is open to the air, radiation is more free. In coils which are in-
closed, the temperature may rise rapidly and unless care is taken,
the insulation may be softened or even burned.
When the heat is dissipated at as fast a rate as it is produced, so
that the temperature of the resistor remains constant, the resistance
becomes constant.
Equation (2) is TF= JH=RIH (2)
Since from Ohm's law, I=E/R we may write
W=JH^R^^t~t (32)
E
Again substituting R= j >
we have W=^ JH-^J =^EI t (33)
These three equations will give the energy in joules when am-
peres, ohms, volts, and seconds are used.
Power is the time rate of change of energy. If the three equations
above are divided by the time <, we have the corresponding three
equations for power.
W
P=j=RP (34)
=B'IR (35)
=EI (36)
Exercise 1. What power is required to operate 1000 incandescent lamps, each of
which requires i amp. and 110 volts?
First solution.— Yrom equation (36), each lamp requires
iX 110= 55 watts.
For 1000 lamps—
■ lOOOX 55= 55,000 watts
= 55kw.
RADIO COMMUNICATION.
TW wstts— 1 horsepower,
» of each lamp Is glvan hj
/■-220Xl-MwatU
F-lOOOX.'iS-.TSkw.
F, Capacitance.
29. Dieleottlc Conent.— So (ar, only steady currenta and their
flow in conductors have been considered. In a perfect iiunilatiiig
mat«rial, current can flow only momentarily. It an electromotive
force ia applied between two points of an insulator, a momentary
flow of current takes place which soon ceaaea. The current flow ia
very different from that in a conductor. If a very senaitive indicator
of current g, Fig. 46, ia connected into the circuit, it shows aeudden
deflection when the key ia cloaed. This deflection soon drops to
zero. The momentary flow of electricity ia due t« the production of
72 RADIO COMMUNICATION.
a sort of electric strain or ''displacement" of electricity. This is
resisted by a sort of elastic reaction of the insulator that may be
called electric stress. On account of this reaction of the electric
stre^, the electric strain due to a steady applied emf. reaches a
steady value, and the current becomes zero. When the electric
strain is subsequently allowed to diminish, a current again exists in
the opposite direction. A current of this kind, called a, "displace-
ment current," exists only when the electric strain or displacement
is changing. When considering the existence of electric strain or
displacement in an insulating material, the material is called a
''dielectric," and the displacement current is sometimes called a
"dielectric current."
We do not think of this electric displacement as being due to the
actual passage of matter, on which the charge is carried from one
plate to the other, nor even from one molecule to another within the
substance. It is rather as if, in each molecule, a positive charge is
moved to one end and a n^ative charge to the other. Then with all
the positive charges pointing in one direction, the effect is that a cer-
tain change has been transmitted clear across the dielectric. An
illustration may aid in making this idea clearer. In a dense crowd of
people, a sudden push or shove on one person will be sent through
from person to person. Energy is transmitted, and yet no single
person has passed all the way across.
When a dielectric is in the electrically strained condition, it
possesses potential energy in the "electrostatic " form. (For a brief
discussion of energy, see C. 74, p. 9.)
30. Condensers. — Displacement is produced in a dielectric by
placing the dielectric between metal plates and connecting a battery
or other source of emf. to these plates. Such an arrangement con-
sisting of metal plates separated by a non-conducting material is
called a condenser. Thus in Fig. 47, A and B are the metal plates
of the condenser. The dotted lines indicate the directions of the
electric strain or displacement. The plate from which the displace-
ment takes place is called the positive or + plate of the condenser.
Conversely, the other plate is called the negative or — plate. The
dielectric may be air or other gas, or any solid or liquid that is not a
conductor. When the battery is connected to the condenser, a
displacement current begins to flow, continuing until the electric
displacement reaches its final or steady value. The displacement
produced depends upon (a) the voltage applied to the condenser
RADIO COMMUNICATION. 73
and (6) the kind of dielectric. A continuous or direct current can
flow only in conductors. An alternating current, in which the
direction periodically changes sign, can flow also in condensers in
the form of a dielectric current. (See Sec. 58.) In this case, the
electric strain or displacement reverses its direction with every
reversal of the current. The existence of the electric strain or
displacement in the dielectric is equivalent to the presence of a
certain quantity or charge of electricity.
For a given condenser, its charge Q is found to be directly propor-
tional to the applied voltage E. This relation may be written
Q==CE (37)
where C is a constant. For any given condenser the value of this
constant is seen to be the ratio of the charge to the voltage, or
C=| (38)
This constant is called the "capacitance" of the condenser. The
units used for capacitance are the "microfarad" and the "micromi-
crofarad," abbreviated as "mfd." and "micro-mfd." (See defini-
tion in Appendix 2, p. 350.)
The capacitance changes when different dielectric materials are
used. If the plate area is increased, the capacitance increases in
direct ratio, and as the plates are brought closer together, the capaci-
tance increases. (Formulas for calculating the capacitance of con-
densers are given in C. 74, p. 235.)
Charging of Condensers. — During the brief time in which the
charge is accumulating in a condenser, the voltage -p due to this
charge is increasing. This voltage tends to oppose the applied or
, Q
charging voltage. When -p has become equal to E, the charging
process comes to an end. It will be noticed that equation (37) does
not contain a time factor; therefore the same amount of charge is
stored in a condenser whether it is built up slowly or quickly . How -
ever, the rate of building up the charge depends upon the value of
the capacitance and resistance of the circui t . The larger the product
of the factors C and R the greater is the time required to arrive at any
given fraction of the applied voltage; this product OR is called the
time constant of the circuit.
74 RADIO COMMUNICATION.
31. Dielectric Properties. — A simple experiment will show that
the charge accumulated in a condenser, for a given voltage and dis-
tance apart of the plates, depends upon the kind of dielectric mate-
rial. A pair of plates with dry air between them is charged by a
certain emf . , and the quantity or amount of charge is measured by
some suitable means. If now a slab of paraffin be inserted between
the plates, it is found that for the same voltage the charge is in-
creased. Denoting the capacitance with air by C^ and the capaci-
tance with paraffin by Cp, we may write
where ^is a constant. By simply changing the dielectric material,
and without changing the geometric arrangement of the plates, we
find that the capacitance has been increased. Air is commonly used
as the standard of comparison, and the factor ^is called the " dielec-
tric constant" ^ of the material. The dielectric constant of any sub-
stance may then be defined as the ratio of the capacitance of a condenser
using this substance as the dielectric, to the capacitance of the same con-
denser vjith air as the dielectric. This ratio is seen to be the factor by
which the capacitance of an air condenser must be multiplied in
order to find the capacitance of the same condenser when the new
substance is used. Some values are given below.
Substances.
Paper, dry
Paper (treated as used in cables)
Paraffin
Ebonite
Petroleum
Transformer oil
Mica
Glass
Water
Values of
dielectric
constant.
1.5
4
2 to 3.3
2to3.2
2.1
2.5
4 to 8
4 to 10
81
A wide variation is seen in the values given for some substances,
inasmuch as the properties of such materials differ greatly with the
rapidity or slowness with which the charge is applied or withdrawn.
Quite different values of ^will be found, if the measurements are
made with a rapidly reversed voltage and with a slowly applied
1 Sometimes called also "inductivity" or "specific inductive capacitance."
RADIO COMMUNICATION. 75
voltage from a battery. For accurate values, the conditions of use
must be very precisely stated.
Dielectric materials are not perfect insulators, but do have a very
small electric conductivity. A condenser will permit a very small
current to flow through it continuously when a voltage is applied
to its terminals, and it will discharge itself slowly, if allowed to stand
with its terminals disconnected . This is called the ' ' leakage ' ' of the
conden ser . Materials differ greatly in this respect. A pair of plates
with dry air as dielectric will retain the charge almost indefinitely
after the voltage is cut off, while in some paper condensers the charge
disappears by leakage in a few minutes.
If an emf . gives a condenser a certain charge when applied for a
short time, and a greater charge when applied for a longer time, the
dielectric is said to possess " absorption. ' ' There is a gradual pene-
tration of the electric strain into the dielectric, which requires time.
When the terminals of a charged condenser are connected by a con-
ductor, a current flows and the condenser discharges. The charge
which flows out instantaneously upon discharge is called the " free
charge." With some dielectrics, if the terminals are connected a
second time, another and smaller discharge occurs, and this may be
repeated several times. This so-called residual charge is due to the
absorbed charge, and indicates a slow recovery of the dielectric from
the electric stress. In condensers made with oil or well selected
mica for the dielectric, absorption is small. It is larger with glass,
and very troublesome with bakelite and similar materials. After
charging such a condenser with a high voltage, the absorbed charge
continues to be given up for a long time. Absorption is accompanied
by the production of heat in the dielectric. This represents a loss
of energy.
The ratio of the free charge of a condenser to the voltage across its
terminals is called the "geometric capacitance." Any measure-
ments of capacitance which make use of a prolonged time of charging,
yield values larger than the geometric capacitance. Measurements
made with high-frequency alternating currents give values which
approach closely to the geometric capacitance.
Summary. — ^An elastic body is distorted or strained by placing it
under the action of a stress; and the effect produced is measured in
terms of the flexibility of the material. A dielectric substance is
strained electrically by placing it under the action of an emf. , and
the effect produced is measured in terms of the capacitance of the
76 RADIO COMMUNICATION.
condenser. It is of interest to note that the capacitance of an electric
condenser is directly analogous to flexibility, or stretchability of
an elastic body.
32. Types of Condensers. — In order to increase the capacitance
of a condenser, we may —
1. Increase the area of the plates.
2. Diminish the distance between the plates.
3. Use a substance of larger dielectric constant.
In general, condensers are classified in two groups, as they may
be designed respectively, for (a) low voltage — less than 500 volts,
or (b) high voltage — several thousand volts. Increasing the plate
area tends to increase the bulk and weight of the condenser. Bring-
ing the plates very close together makes necessary the use of a sub-
stance of high dielectric strength if the voltage is high . For low volt-
age service, where large capacitance is essential, the condenser plates
are made of tin foil with thin sheets of mica or paraffined paper between
them. The sheets are piled up as shown in Fig. 48, p. 71. The
dielectric layers are represented by oa, and the two sets of conducting
plates by 66, and cc, respectively. These are pressed into a com-
pact form and held in place by a clamp, flowing the entire set of
plates with melted paraffin or wax. If the condenser must withstand
a very high voltage, the plates will be more widely separated and
usually air or oil is used as the dielectric. If it is desired to have the
capacitance of the condenser variable instead of fixed, the construc-
tion usually takes the form shown in Fig. 49. Two sets of inter-
leaved plates are insulated from each other, and one set is mounted
80 that it can be rotated with respect to the other. Such a condenser
can be calibrated so that the capacitance corresponding to any
angular setting of the rotating part is known. Condensers used in
radio circuits are represented by certain symbols. These may be
found in Appendix 3, page 354.
It is not always necessary that the conducting plates in the
condenser should be sheets of metal. The earth is a conductor
and frequently replaces one plate in the system. A wire stretched
on a pole line forms one plate of a condenser, and the other plate
may be the neighboring return wire of the circuit, or it may be-
the earth itself. Several wires in a connected group will have
more capacitance with respect to the earth than a single wire.
Such a condenser is the radio antenna. (Fig. 50.) The conduct-
ing core of a submarine cable forms one plate of a condenser, the
insulating material is the dielectric and the sea water is the other
RADIO COMMUNICATION.
77
plate. Similarly in a telephone cable, paper is the dielectric, and
any single conductor of the cable may be regarded as one plate,
the other plate being the adjacent wire of the pair, or the lead
sheath of the cable itself. The great length of such wires and
cables gives them large surface and hence large capacitance. A
mile of standard sea cable may have a capacitance of about J mfd.
A mile of standard telephone cable should not have capacitance
of more than about 0.08 mfd. The capacitance of a pair of No.
8 copper wires, 1000 ft. in length and 12 in. apart is about
0.0032 mfd. Two square plates 10 cm. on a side, separated
FiCa.49
Ptdle Condmnser ef Vari«&ble
^^
V
»
Pia.51
.±J L=.
E.|«ctric ^traun or Dis^lAcem«nT
RaraHcI Wire Antenna
by 1 mm. of dry air have a capacitance of approximately
100 micro-mfd. (For such calculations see C. 74, p. 235.)
33. Electric Field Intensity. — Consider the air condenser shown
in Fig. 51, having an emf. E applied across its terminals. The
emf. is the cause of the electric strain or displacement which is in
the direction shown by the dotted lines. The emf. between the
plates of the condenser is equivalent to a force acting at every
point of the dielectric, which would cause a body having a charge
of electricity to move. This is called the electric field intensity
and is defined as the force per unit charge of electricity. The
space in which this field intensity acts is called an electric field.
78 RADIO COMMUNICATION.
The value of the electric field intensity at any point inside the
condenser ehovn in Fig. 51 is the ratio of the emf. acroHS the
condenser to the distance between tho plat«e. Electric field
intensity & is thus given by
&=| (39)
where £ia the emf. between two points in the dielectric a distance
d apart. £. ia commonly exproaaed in volts per centimeter. It
is a quantity of importance in connection with electric waves.
The electric field in the condenser of Fig. 51 is the same every-
where in direction and in value. This ia called a uniform fifld.
There are many other kinds of fields. The electric field about
two small unlike charges ia shown in Fig. 52. Another example
is given by two iKKlies, one of which is a long vertical wire, and
the other ia a conductor extended in a horizontal direction. These
amount to two conductors separated by a dielectric (air), thus
fulfilling the definition of a condenser. Suppose the lower body
is the earth itself, which ia a conductor. The field about the
Bj-Btem will he repreaented by Fig. 53. This representa the form
of condenaer and electric field in the oaae of the radio antenna.
34. Energy Stored In a Condenser.— The electric strain in the
dielectric of a chaiged condenser represents a store of eneigy. The
amount of energy stored in this way is found as follows. The work
done in placing a charge in a condenser is the product of the charge
by the voltage between the plates. Suppose a condenaer is charged
by applying to it an emf. \(iiich begins at a xero value and riaea
to E volts. The increase in voltage is uniform and hence the
RADIO COMMUNICATION. 79
average voltage is i E. The energy stored in the condenser is the
product of this by the charge, thus
W=i QE (40)
Since Q=CE, from equation (37), we may write
Tr=i cm (41)
The work is expressed in joules when the capacitance is in farads
and the emf. is in volts. A capacitance of 0.001 mfd. charged with
an emf. of 20,000 volts has a store of energy given by
TF=J ^j^X 20,0002=0.2 joules
From equation (41) it appears that time does not enter into the
energy equation. For a given condenser chaiged to a given voltage
it requires the same total amount of energy, whether the charge
is acquired slowly or rapidly.
The total amount of work done in charging a condenser divided
by the time, gives the power expended. This may be written,
or
P=i CE^ N (42)
where T is the time in seconds required to complet^e the charge,
and N is the number of charges completed in one second of time.
If the condenser in the above problem is charged by a generator
giving an alternating emf. with a frequency of 500 cycles per
second, the power becomes
P=i C^^J\r=0.200X1000=200 watts.
It will be noted that the condenser is charged and discharged
twice in every complete cycle of the a.c. generator; also that E is
the maximiun emf.
35. Condensers in Series and in Parallel. — ^Just as it is sometimes
found convenient to combine resistances into series or parallel
groups, so it is often desirable to combine condensers. The capaci-
tance of the group, however, is not calculated the same way as in
the case of resistances.
Condensers in Parallel. — Fig. 54 shows three condensers con-
nected in parallel. The condensers are all under the same im-
pressed emf., and they accumulate charges proportional to their
80
RADIO C03r:MUNICATI0N.
respective capacitances. It has been stated in Section 30 that
capacitance is proportional to plate area. Connecting condensers
in parallel is equivalent simply to increasing the plate area. If Cj
C2, C3, etc., represent, respectively, the capacitances of tJie conden-
sers of the group, and if C represents the equivalent capacitance of
the entire group, we may then write
C=Ci + C2+C3+ . . . (43)
Parallel connection of condensers always gives a larger capacitance
than that of any single member of the group.
Condensers in Series. — If several condensers are connected as shown
in Fig. 55 they are said to be connected in series. In finding the
equivalent capacitance of such a group, it must be kept in mind that
F10.54
^\
£^
^^
^h
Ci
c«
c»
^NI^I^I^1^H
Cor\defvs«r» in PamIUI
^m
hHH
Cond«rvs«ra in ^«ri«s
FJQ.55
the same charge is given to each condenser, and that the total voltage
E is subdivided among the condensers in direct ratio to their capaci-
tances. Using symbols as above we may then write
E=E,+E,+E,+ ...
or since in general E=-7^
7^ — TT~r f^ ~r /-I ~r
\y \y\ \.-'2 ^Z
Whence 7»=77 + ?t+7^+ • • • i^)
U L/j ^2 t^3
Series connection of condensers always gives a smaller capacitance
than that of any single member of the group. (See problems below.)
1. A condenser has a capacitance of 0.014 mfd., and it is charged with an emf.
of 30,000 volts.
Find (a) the charge in the condenser, (6) the energy stored, (c) the power expended
when charged by a 500-cycle a/C. generator.
RADIO COMMUNICATION.
81
2. A condenser is built up of 15 parallel and circular plates. Each plate is 20 cm. in
diameter and the separation is 1 mm. Petroleum is used as a dielectric. Calculate
the capacitance. (See C. 74, p. 235.)
3. Three condensers have capacitances of 0.02, 0.20 and 0.05 mfd., respectively.
Find the equivalent capacitance, (a) when they are all in series; (&) when they are
all in parallel.
G. Magnetism.
36. Natural Magnets. — One of the forms in which iron is found in
the earth is the black oxide of iron (chemical formula Fe304), called
magnetite or magnetic iron ore. A piece of this substance is called
a "natural magnet," and it has two very remarkable properties as
follows:
(a) If a piece of it is dipped into iron filings the filings will adhere
to it. *
(6) If a piece of it is suspended by a silk thread, or by a thin
imtwisted cord, it will set itself with its longer axis very nearly in a
north and south direction.
37. Bar Magnets. — ^A small rod of iron or steel which is brought
near to a piece of magnetite, or which is rubbed on it in a certain
FiO.Sfe
1
Ma^ne^dm by f-h* Electric
FIO.57
Pivoted M^^sf lo
J
way, shows the same properties, and is eaid to be ''magnetized."
If the rod or bar is made of rather hard steel, the effect persists after
the iron ore has been taken away, and the magnetized rod is then
called a "permanent magnet," or simply a bar magnet. These
permanent magnets may be made in the form of straight bars of round
or square section, usually with the length rather large as compared
to the diameter. They are also often bent into various shapes, a
common form being the horseshoe or U-shaped magnet.
97340"— 19 6
82 RADIO COMMDXICATION.
Magnets may also be made by paasing an electric curreQt through
a coil ot wire which surrounda the rod. (See Fig. bS.) If the rod ii
made of soft iron, it is only magnetized as long as the current Rovm.
It is then called a temporary magnet or an "electronwgnet." Ex-
amples ot electrom^nets are seen in induction coil and buzzer cores,
in telegraph soundeis and relays and in telephone receivers. Elcc-
trom^neta are very useful because the magnetism ia bo easily con-
trolled by variations in the current strength. It the bars are of
hardened Bicel, the magnetism due to the current remaiua after the
current ceaeea and a permanent magnet is the result.
A slender magnetized steel rod mounted carefully on a pivot
(Fig. 67) will turn very nearly into the north and south position, and
is called a "compaas needle." It is used by Bailors and surveyors
for determining directions. The end which points north is called
Fi<a s»
, , ,■ _ ^ -, . . , Fia.fio
'^y ^^ .J lIC
by irpn fili-ija
the north-pointing or simply the "north pole." The other end ii
called the south pole.
38. The Uagnetic Field. — If a compaas needle is placed at various
poaitlonB near a lar);e bar magnet, it changes its direction aa shown
in Fig. 58. Thia shows that in the space all around the magnet
there are forces which act on magnetic polefl. If iron filings are
RADIO COMMUNICATION. 83
sprinkled on a level sheet of paper which lies over the magnet, the
filings arrange themselves as shown in Fig. 59. Each little par-
ticle of iron acts like the compass needle and points in a definite
direction at a given position. These direction lines, called "mag-
netic lines of force,'* all appear to center in two points near the ends
of the bar magnet. These points are called the " poles " of the mag-
net. Two magnetic poles are said to be alike when they both
attract or both repel the same pole. If one attracts and the other
repels the same pole, they are said to be unlike. Like poles repel
each other and unlike poles attract each other. It is then easy to de-
termine which is the north and which is the south pole of a bar
magnet by means of the direction in which the north pole of a
compass needle points.
The region all about a magnet, in which these forces on the poles
of magnetic needles may be detected, is called the "magnetic
field." The intensity of a magnetic field may be defined in terms
of the force which acts on a given magnetic pole, or it may be de-
fined in another way, as described in a following paragraph. The
direction of a magnetic field is defined as the direction in which
the north pole points.
The earth has a ma^etic field about it which is represented by
Fig. 60. This field is similar to that which exists about a bar
magnet placed within the earth with its ends at the North and
South Poles of the earth.
39. Magnetic Flux and Flux Density. — ^The arrangement of the
iron filings in Fig. 50 shows that there is a greater effect at some
points than at others. It also suggests that the lines of force may
be thought of as similar to stream lines in a moving fluid. From
this point of view there is said to be a magnetic flux through the
space occupied by the magnetic field. This is represented by
lines drawn closer together where the field is strong and farther
apart where the field is weak. The magnetic field must not be
thought of as made up of filaments, like a skein of yam, because it
really is continuous. However, electrical engineers represent a
magnetic flux by drawing one line through the field for each unit of
the flux. The number of such lines through each square centimeter
of the field perpendicular to the lines is the ** magnetic induction "
or "flux density." The unit of flux density exists in a magnetic
field when the imit of magnetic flux is distributed over a square
centimeter of area, taken perpendicular to the direction of the flux.
84 hadio cojijiusicatiox.
40. Tlie Uafnetlo Field abont a Ciuieiit. — It haa already been
pointed out in Section 3 that there is a magnetic field about a vire
in which a current is flowing. ETcperiments with the compass show
that this mapictic field has lines of force in the form of concentric
circles about the wire. These circles lie in planea at right angles
to the axis of the wire. It the wire is grasped by the right hand
with the thumb pointing in the direction of the current, the fingers
will show the direction of the magnetic field (Fig. 10). This field
extends to an indefinite distance from ,the conductor, but for points
farther from the wire the effect becomes more feeble, and the more
aonaitive must be the apparalus for detecting it. If the current
/.';V:'~^--,\ f"'^*'
Fia»
m
IW«lfcn;iJib..t*«„y.
Fia-CT
k<-in.ti.: FiJd ^
Joler-tlrf
st«])B, the magnetic field, together with its effecta, disappears. When
current ia started through the wire, we may think of the magnetic
field aa comii^ into being and sweeping outward from the axis as a
center. This disappearing and rebuilding of the mc^etic field
as the current dccreaseB and increases will be made use of in Sec-
tion 46, in explaining some important principles which apply in
radio circuits.
41. The Solenoid and the Electromagnet. — If the wire which
carries acurrentis bent into a circle, the magnetic field ia of the form
shown in Fig, 61. At the center of the circle the field is uniform
only tor a very small area. It many turns are wound close together
RADIO COMMUNICATION. 85
in what may be called a bunched winding, the intensity of the
magnetic field is increased in direct proportion to the number of
turns. When the wire is wound closely with many tiu*ns, side by
side along the surface of a cylinder, the coil is called a "solenoid,**
Fig. 62. In this case, the magnetic field is nearly uniform for a con-
siderable distance near the center of the coil, and the solenoid has
the properties of a bar magnet. This is seen by comparing the
magnetic fields of Figs. 63 and 59. The intensity of the field and
the magnetic flux density within the solenoid, depend entirely upon
the strength of the current and the number of turns of wire per centi-
meter. The same magnetizing effect can be secured with many
turns and a weak current, or with a few tmns and a strong current,
provided only that the product of wire tiuns times amperes of cur-
rent is the same in each case. This product is called the **ampere-
tiu'ns.** In round numbers the magnetizing field strength, repre-
sented by the symbol H, is given by
rr 5 /ampere-turnsX ,_.
-^=4 V" -length— ; ^'^^^
If / is the current in amperes the accurate formula may be
written *
42. Magnetic Induction and Permeability. — If the space within
the solenoid is filled with iron, the magnetic flux lines are very
greatly increased. This is due to a property of iron called magnetic
' * permeability. ' ' To say that iron is more permeable than air means
that the magnetism is stronger when iron is present than it would
be if the space were filled with air alone. ^ Permeability varies
according to the quality of the iron, from a few units to a few thou-
sand. For example, to say that the permeability of a certain sample
of iron is 1000 means that the magnetic flux through 1 cm. of
cross section of the iron is 1000 times as great as the flux through
* For proof of this formula see C. 74, p. 15.
' Time is required for the magnetization to travel inward from the surface to the
axis of the iron core. Hence, if the current is rapidly reversed in direction, the mag-
netic wave started by one-half cycle does not have time to travel inward appreciably
before the reversed half cycle recalls it and starts a wave of opposite sign. As a con-
sequence the magnetism is confined to the outer layers of the iron core. For this
reason iron is not as effective in increasing the number of flux lines in high frequency
circuits, as it is with steady currents or low frequency currents.
S6 RADIO COMMUNICATION.
the same area before the iron was present. The total magnetic flux
through an iron core within a magnetizing coil, divided by the area
of cross section, gives the "magnetic induction," which is repre-
sented by the sjTnbol B. We may denote total flux through the
iron by ^j, then
<t>i=BA (47)
where A is the area of cross section of the iron core. If the intensity
of the magnetizing field within a solenoid is denoted by H, then the
total magnetic flux through the solenoid is given by
<t>^=nA (48)
where A is the area of cross section and ^^ is the total flux through
the air core. The permeability is defined as the ratio of B to H^
It is important that the student should remember that the mag-
netic induction depends upon (a) the number of ampere-turns and
( 6 ) the property of iron called permeability. The number of ampere-
turns is under the control of the operator. The permeability de-
pends upon the quality of the iron itself.
If the current in the windings is reversed, the direction of the
magnetic field is also reversed. The student should learn at least
one rule for remembering the relation between the direction of the
current and the direction of the magnetic flux. Two such memory
helps are here given.
(a) Look along the direction of the lines of magnetic flux through
the solenoid, and the current is in a clockwise direction.
(b) Grasp the solenoid with the right hand, the fingers pointing
along the wires in the direction of the ciurent. The thumb then
points in the direction of the magnetic flux inside of the solenoid.^
43. The Force on a Conductor Carrying Current in a Magnetic
Field. — If two different magnetic fields are brought together in the
same space, with their directions parallel, a force is always de-
veloped. If the lines of magnetic flux are in the same direction,
the two fields mutually repel one another, and if the flux lines are
in opposite directions the two fields will be drawn together. WTien
a ciurent flows in a wire which is at right angles to a magnetic
field, a force will act on the wire. A rule which will help the
student to remember the direction of the motion, together with
1 Apply each of the above rules to Fig. 62. Also wind an experimental solenoid
with a few feet of wire, connect it to a dry cell and mark in some way the direction
of current through the windings. Test its polarity with a compass, remembering
that like poles repel and unlike poles attract.
RADIO COMMUNICATION. 87
the directions of current and field, is the so-called "left-hand
rule." Extend the forefinger of the left hand in the direction of
the magnetic field, and hold the middle finger at right angles to
it in the direction of the current. The extended thumb, held at
right angles to both the other directions, indicates the direction
of the motion. Note that this rule calls for the use of the left
hand. Compare this with the right hand rule of Section 45.
When the wire which carries the current is at right angles to the
direction of the magnetic field, the pushing force on the wire is equal
to the product of the current, the intensity of the magnetic field, and
the length of wire which lies in the magnetic field.
If the wire makes some other angle with the direction of the mag-
netic field, the direction of the force is still the same as for the right
angle position, and the value of the force is smaller. In the single
instance that the direction of the current coincides with the direction
of the magnetic field the force is zero.
This push on a single wire is in most cases small, but by arranging
many wires in a very intense magnetic field, very large forces may
be obtained. The powerful turning effect of an electric motor
depends upon these principles. (See Sec. 96.)
H. Inductance.
44. The Linking of Circuits with Lines of Magnetic Flux. — ^There
is always a magnetic field about an electric current. The lines of
magnetic flux are closed exudes and the electric circuit is also closed.
The lines of magnetic flux are then thought of as always interlinked
with the wire turns of the circuit. (See Fig. 64. ) The number of flux
lines through a coil will depend upon the current, and any change in
the current will change the number of linkings. If there are two
turns of wire the circuit will link twice with the same magnetic flux,
and so, for any number of turns, the number of linkings increases
with the number of turns. Let <t> represent the number of magnetic
flux lines, N the number of linkings and n the number of wire turns.
Then it is seen that the number of linkings is always given by
N=n <t> (49)
A change in N may be brought about by (a) a change in <t>, due to
a change in the current, or (6) a change in the number of wire turns.
Again the loop of wire, Fig. 65, not now connected to any battery,
88
RADIO COMMUMCATIOX.
may be placed near a bar m^net, or a solenoid which has current
flowing in it. Some of the flux lines will pass tlirough the loop.
The number of these flui lines ie represented by * aa before, and
every turn of wire will link with the flux lines. Then the number
of linkingH is given by
JV=
(50)
which is the same expression as in the other case.
The number of flux lines may be changed by changing the number
of wire turns, or by changing the number of flux linea through the
loop. The latter may be done by rotating the loop, or by moving
it with respect to the magnet. If a solenoid is used, the change can
be made by variations in the current through its coils.
45. Induced Electromotive Force. — Whenever there is any change
in the number of liukings between the magnetic flux lines and the
wire turns, there ia always an emf, induced in the circuit. If the
circuit is closed, a current will flow. This is called an induced cur-
rent. Some of the ways in which this is accomplished are de-
scribed in the following paragraphs.
I. A bar magnet is pushed into a closed coil of wire. Fig. 66.
During the time the magnet is moving, there will be indications on
the galvanometer g that current is flowing. When the magnet is
RADIO COMMUNICATION. 89
drawn back, away from the coil, a current is induced in the opposite
direction. The direction of this induced current will always be
such as to oppose the change to which it is due. That is, if the
magnet is approaching the coil, the current will flow in AB so that
^ is a north pole, and hence the magnet will be repelled. If the
key h is open the induced current cannot flow. If it is closed an
induced current does flow, and sets up a magnetic fleld about the
coil. It can be shown that more work is required to move the
magnet with respect to the coil when the key is closed, than when
it is open. These facts are expressed in the law of Lenz, which
states that whenever an induced current arises, by reason of some change
in Unkings, the magnetic field about the induced current is in such a
direction as to oppose the change. A helpful, mechanical illustra-
tion of Lenz's law is seen in the effort necessary to move a stationary
body. Owing to the mass of the body, a force is necessary to start it,
and if one tries to move it suddenly, he will experience a consider-
able reacting force. This reacting force will be greater the more
sudden the change in the motion of the body. Similarly in the
electric circuit, the induced emf . will be greater the more sudden
the change in the number of linkings.
2. The same effects as those described in (1) may be secured if the
bar magnet is replaced by a solenoid carrying current.
3. The effects may also be produced by two solenoids fixed in the
position shown in Fig. 67. If a current is started in one of them,
A, there will be a current induced in the other, which will continue
to flow as long as the current in A is increasing. If the current in
A becomes steady, there is no current induced inB. If the current
in A falls off, the induced current in 5 is reversed in direction. In
all cases it must be remembered that the magnetic field about the
induced current tends to oppose the change that is causing the
induced current.
4. A further example of induced currents is found in the case of
two straight wires, Fig. 68, close together. If the electric current
stops (Fig. 69), starts, or varies in one of them in any way, there are
corresponding induced currents in the other. This case of parallel
straight wires is seen in certain telephone lines where cross talk
occurs, or where there is interference from a.c. power lines. Al-
though we think of the straight and parallel portions of the circuit,
we must not overlook the fact that these are only portions of com-
pletely closed circuits.
90
RADIO COMMUNICATION.
The magnitude of the induced emf, in all of the above cases depends
upon the time rate of change of the number of Unkings. This may be
expressed by the equation
£m/.=f='^ (51)
where t is the time in seconds in which the change n<t> takes place.
This is the basic principle of dynamo-electric machinery.
46. Self Inductance. — With a single circuit carrying current,
as shown in Fig. 64, the magnetic flux which threads through
^^i^
when A currant id «tArt«d er>ata^^«d in
ci'rcwit A.an enn^ I's indvcmd in circuit D>,
Fiq.<&9
Cstrrmrit dteb>in^ in U inducaa
oornsnt in D
Fia.<z»a
CwrrenT st»rTrn^ in A inJocms
Current in t>
1^:^
#^
^&=4
§=#
Fib TO
Circuits i^And & hav« mutual
inductanc*
the circuit (and hence the number of linkings N) is directly pro-
portional to the current strength. This fact may be expressed by
the formula
N=LI (52)
where L is called the ''self inductance," or simply the "inductance'*
of the circuit.
The value of L depends upon the number of wire turns, upon the
shape and size and upon the permeability of the medium about the
circuit. For air the permeability is 1. The inductance does not
depend upon the current which is flowing, except when iron is
RADIO COMMUNICATION. 91
present. By coiling up a piece of ^ire in many turns and intro-
ducing it into the circuit, the inductance of the circuit may b#
greatly increased. In that case the inductance is said to be con-
centrated. It must not be overlooked that the entire circuit has
inductance. This may be distributed more or less uniformly
throughout the circuit.
If a piece of wire is connected to one terminal of a dry cell, and
tapped on the other terminal, a very slight spark may be seen in a
darkened room. If a coil of many turns of "wire is included in series
with this cell, the same process of tapping will show brilliant sparks,
particularly if the coil has an iron core. The explanation of this
lies in the fact that the cell voltage of about 1.5 is too feeble to cause
much of a spark. However, when the large inductance is included
in the circuit, there is a large number of Unkings between wire
turns and flux lines. If these flux lines collapse suddenly, as they
do when the circuit is broken, there will be a large change in the
number of Unkings taking place in a very small interval of time.
From equation (51), this means that a large voltage a\t[11 be set up.
This principle is made use of in ignition apparatus and spark coils-
of various types. According to Lenz's law, the induced emf. will
be in such a direction as to oppose the change which causes it. In
this case, when the circuit is broken, the change is from some value
of current lio zero. Therefore the induced emf. will be in the same
direction as the original current, and will try to keep the current
flowing. On the other hand, when a battery is being connected to
an inductive circuit by means of a switch, the rising current will
establish a set of magnetic flux lines which will, as they grow,
induce an emf. which tends to keep the current from rising.
47. MtLtual Inductance. — Consider a circuit AAy Fig. 70, with a
current / flowing through it. The magnetic flux through A is
directly proportional to /, and that part of the total flux which
Interlinks with a near-by coil B is also proportional to /. This means
that the total number of interUnkings JV, between flux lines that
arise in the A circuit, and wire turns of the B circuit, is proportional
to the current Jin the circuit A. This fact may be represented by
the equation
N^^MI (53)
where M is the constant of proportionality. This factor M is called
the ** mutual inductance" of the two circuits. When currents are
92 RADIO COMMUNICATION.
started, stopped or varied in coil A, the mutual inductance shows
itself b^ an emf. induced in coil B. The induced emf. may be
calculated by
JS;=J/y (54)
where I^ is the amount by which the current in the A circuit varies
in the time t.
In radio circuits the mutual inductance is often used to transfer
power from one circuit to another when there is no conducting patJi
between them.
48. Energy Belations in Inductive Circuits. — In mechanics it is
well known that a piece of matter cannot set itself in motion and
that energy must be supplied from outside. So in the electric
circuit, a current cannot set itself in motion, and energy must be
supplied by some form of generator (source of emf.). It has already
been explained how a magnetic field arises about electric circuits.
When this field collapses or disappears, the energy stored in the
field is returned to the circuit. It can be shown that the energy
thus associated with a magnetic field is given by the equation
Tr=JLJ2 (55)
where F is the value of the current and L is the self inductance.
The student who is familiar with the laws of mechanics will note
that this equation is quite similar to that for kinetic energy of a
moving body
Kinetic energy=JiiM2
where m is the mass of the body and s is its speed.
Illustration of Inductance. — \\Tien a nail is forced into a piece of
wood, the mere weight of the hammer as it rests on the head of the
nail will produce but little effect. However, by raising the hammer
and letting it acquire considerable speed, the kinetic energy stored
is large, and when the motion of the hammer is stopped this energy
is used in forcing the nail into the wood. In the electric circuit a
cell with its small emf. can cause only a feeble spark. By including
a piece of wire with many turns in the circuit, however, energy is
stored as shown in equation (55). A small current will enable a
large amount of energy to be stored in the magnetic field, if L is
large. Then when the circuit is broken and the field collapses, this
large amount of energy is released suddenly, and a hot spark of
considerable length is the result.
RADIO COMMUNICATION. 93
The close relations between capacitance, inductance and resist-
ance will be more fully discussed in Chapter 4.
I. Alternating Current.
49. Beactance. — ^A steady current in a circuit meets no other
hindrance than the resistance of the circuit. If the current changes,
this is no longer true. If the circuit has inductance, the current
is opposed by the emf. induced by the variation of the current.
(See Sec. 46.) If a condenser is present, this is constantly charging
or discharging as the current changes, and it exerts a controlling
influence on the passage of the cvurent. If both inductance and
capacitance are included in the circuit, they tend to offset each
other in their effects, but usually one or the other exerts a pre-
dominating influence, with the result that there is added to the
resistance an extra opposition to the current, which is known as
the "reactance."
The more rapid the changes of the current, the greater the induced
emf. in a circuit and consequently the greater the inductive re-
actance. On the contrary, the reactance of a condenser is less,
the more rapidly the current varies, as can be understood when we
reflect that the greater the number of charges and discharges of the
condenser performed each second, the greater the total quantity
of electricity which flows around the circuit in that interval, that is,
the greater the current. In general, the reactance of a radio circuit
is very much greater than the resistance.
To calculate the current in a radio circuit, then, it is necessary
.to know how to calculate the reactance and how to combine it with
the resistance, in order to determine the total hindrance or "im-
pedance" to the current. Since the reactance, however, depends
upon the way in which the current is varying, it is evident that this
must be definitely specified in each case. The problem cannot be
solved for all imaginable kinds of variation of the current. Radio
currents, however, belong to the general class of alternating currents,
and for these, the theory is rather simple. In the following sections
is given a brief treatment, not of general alternating current
theory, but merely of those alternating current principles which
are essential to an understanding of the actions in radio circuits.
50. Nature of an Alternating Carrant. — ^An alternating current is
one in which electricity flows around the circuit, first in one direction
and then in the opposite direction, the maximum value of the
94
RADIO COMMUNICATION.
current in one direction being equal to the maximum value in the
other. All the changes of current occur over and over again at
perfectly regular intervals.
Sine Wave. — To get an insight into the nature of such a current,
suppose a case where the alternations occur so slowly that we may
follow the changes of current with an ammeter. In the table below
are given values of the so-called **8ine wave current" at successive
equal intervals of time. The maximum value is taken as 10 amp.
Time
Current 1
Time
Cmrenl
Time
Current
(sec).
(amp).
(sec).
(amp).
(sec).
(amp).
1
13
- 2.59
25
2.59
1
2.59
14
- 5.00
26
5.00
2
5.00
15
- 7.07
27
7.07
3
7.07
16
- 8.66
28
8.66
4
g.66
17
- 9.66
29
9.66
5
9.66
18
-10.00
30
10.00
6
10.00
19
- 9.66
31
9.66
7
9.66
20
- 8.66
32
&66
8
8.66
21
- 7.07
33
7.07
9
7.07
22
- 5.00
34
5.00
10
5.00
23
- 2.59
35
2.59
11
2.59
24
36
12
The ammeter in such a case would creep slowly up to a maximum
indication of 10 amp. , return gradually to zero, reverse its direction
and build up to a value of 10 amp. in the opposite direction, then
decrease to zero again, build up again in the original direction, and
so on. It is, of course, to be understood that the current assumes in
turn all possible values between zero and the maximum value (10
amp. in this case), and that the current has the same value through-
out the circuit at every moment. The current in this case, as well
as that of a steady current, may be regarded as like the flow of an
incompressible fluid. The emf. is, however, to be regarded here as
a variable electric pressure, which acts first in one direction and
then in the other.
The values of current in the preceding table are plotted in Fig.
71 as ordinates (vertically), and the corresponding lengths of time
elapsed since the start, as abscissas (horizontally), and a smooth
curve drawn through the points enables one to determine what is
the value of the current for any moment lying between any two of
those which are included in tne table. It is to be noted that the
changes of current repeat themselves. Thus in the table the current
is the same at 1 sec. and 25 sec. after the start; at 7 sec. and 31 sec,
HADIO COMMUNICATION. 95
etc. The interval of 24 seconds in this example is the "pericNi"
of this alternating current. The current, paseea through a complete
"cycle" of changes in one period.
A current like that just treated is the same ae that which would
be produced in a circuit attached to a coil revolving very slowly
in a uniform magnetic field. (See Chap. 3, Sec. 62.) The motion
has been assumed slow in order that the clmnges can be followed
with ordinary direct current instruments. In order to represent
the current developed by an ordinary low frequency alternating
current generator, we must, however, imagine the coil to revolve
more than a thotutand times more rapidly. Thus the usual a.c.
lighting circuits Carry currents whose period ie only about -^ second.
The current passes lirough 60 complete cycles each second, that ia,
its "frequency" is 60 cycles per second. Ordinary alternating-
current generators cannot use magnetic fields which are entirely
uniform, so that the current obtained never paasea through its
changes in exactly the same way as the ideal sine current pictured
in Fig. 71. The difference is, however, usually so small in well-
designed machines tliat it does not need to be taken into account.
The frequency of radio currents is enormously greatsr than the
usual low frequency alternating currents. In order that Fig. 71
may properly represent a radio current, we must suppose a whole
cycle to be completed in, say, TencTiBu to tWirair second.
51. Average and Effective Values of Altenuting Current.— In just
the same way as we have analyzed alternating current by imagining
it to change slowly, it is possible to get an insight into complicated
movements, like the throwing of a ball or the galloping of a horse,
by running a motion-picture film of the action so slowly that the
separate pictures on the film can be examined one at a time.
96 RADIO COMMUNICATION.
When a direct current ammeter is traversed by an ordinary alter-
nating current, the changes of current are altogether too rapid to be
followed by the needle of the instrument. It can only take up an
average position corresponding to the average of all the values
through which the current passes during a cycle. However, since
the current passes through the same values in one direction that it
does in the other, the average value during the cycle must be zero.
That this is the case can be shown by connecting a direct current
ammeter into an alternating current circuit. The ammeter needle
stands still at zero, or else merely presents a blurred appearance
while standing at zero. The same remarks apply to the use of a
d.c. voltmeter in an a.c. circuit.
A.C. Voltmeters and Ammeters Indicate Effective Values. — ^Alternat-
ing current voltmeters and ammeters may be of several different
types (hot wire, dynamometer or electrostatic, see Sec. 60), all
of which, however, give a deflection in the same direction which-
ever the direction of the current. The force on the moving portion
of such an instrument is, at every moment, proportional to the
square of the current through the instnunent. When an alternat-
ing current passes, the average deflection taken up by the pointer
is, therefore, proportional to the average of the squares of all the
values of current during the cycle. For a true sine current, the
average of the squares of all the values of current during the cycle
can be shown to have a value of one-half the square of the maximiuu
value.
Equivalent Direct Current. — The heating effect of a current is, at
every moment, proportional to the square of its value at that moment.
The average heating effect of an alternating current must, therefore,
be proportional to the average of the squares of all the values of the
current during the cycle, or must be proportional to one-half the
square of the maximum ciurent. The same heating effect would, of
course, be produced by a steady current, whose square is equal to
the average of the squares of the alternating current taken over the
whole cycle. That is, the *' effective current*' is equal to the value
of the direct current which would produce the same heating effect
in the circuit in question. Since its square is equal to one-half the
square of the maximum value, the effective value of the current is
r=V
(maximum)^ .-gv
RADIO COMMUNICATION. 97
orequal to the maximum value divided by V2. This is the same as
the maximum value multiplied by 0.707.
The effective current in the table above is 7.07 amp., and this
would be the current indicated by an a.c. ammeter in the circuit,
although the current varies between 10 amp. in one direction and 10
in the other. The same heating effect would result if a direct cur-
rent of 7.07 amp. were sent through the circuit. Likewise, an a.c.
voltmeter will always read the effective value of the voltage, which
is equal to the maximum voltage multiplied by 0.707.
52. Circuit with Resistance Only. — Let us imagine a circuit with
resistance R ohms, and with such small inductance and capacitance
that they may be neglected. Let us suppose, further, that sine
wave alternating emf. is applied to the circuit. At every moment,
the current will be found by dividing the emf. at that instant by
the resistance of the circuit. The current is zero at those moments
when the emf. is also zero, and is a maximum when the emf. is a
maximum. In fact, the changes of current keep step with those of
emf. The current and emf. are said to be "in phase" or to have
**zero phase angle.'* Since the effective values of 'emf. and current
are each the same fraction of their respective maximum values, the
effective current / will be calculated from the effective emf. E by
the relation
^ E
I=fi (57)
That is, in this special case, Ohm's law holds, even when the cur-
rent is alternating- An ordinary incandescent lamp circuit approx-
imates this ideal circuit.
The power in the Circuit is, at every moment, equal to the product
of the values of current and emf. which hold at that moment. The
average power taken over the whole cycle is equal to the product of
the effective current by the effective emf., that is, average P=IE.
The power is used up in the circuit entirely in heating the resistance
R.
53. Phase and Phase Angle. — The values of current given in the
table above are those which hold for certain definite moments in the
cycle of change of the current. Each time the cycle is repeated,
the same values are run through, and any chosen value will be
reached at a perfectly definite fraction of the way through the cycle.
Each maximum in the ix)sitive direction, for example, occurs just
97340°— 19 7
98 RADIO COMMUNICATION.
one-quarter of a cycle after the preceding zero value. The points A
in Fig. 71 have the same phase, although each is in a different cycle
from the others. The current has the same value at the points C
as at .^, but points C are not in the same phase as A, since at A the
current is increasing, and at C it is decreasing.
The phase is, then, a certain aspect or appearance, occurring at
the same definite part of each succeeding cycle. Difference in
phase is nothing more than difference in position in the cycle. It
is best referred to as difference in time, expressed as the fraction of
the length of a cycle. Thus, the difference of phase of points B and
0, Fig. 71, is one-quarter of a cycle; that of points B and D one-half
cycle, etc. It is also customary to express difference in phase as an
angle. A difference of phase of one complete cycle is regarded as
equivalent to the angle of a whole revolution or circumference, that
is, to 360°. One-quarter cycle is accordingly 90°, and two points
with a difference of phase of one-quarter cycle are said to have a
difference of phase of 90°, etc.
The idea of phase angle is useful when two emfe. are acting
in the same circuit or when the current and the emf . which pro-
duces it do not pass through their maxima at the same moment.
Fig. 72 shows the waves of emf. and ciurent in a circuit where the
emf. and current differ in phase by about one-eighth of a cycle;
i. e., they have a phase angle of about 45°.
When a circuit has resistance but no inductance or capacitance,
the emf. and current are in phase or the phase angle is zero. Their
waves, shown in Fig. 73, pass through zero at the same moments
and reach their maximum values at the same moments.
-The case of opposite phase shown in Fig. 74, in which two emfs.
are represented, is such that, although they pass through their zero
values at the same moments, at other times one is always acting in
the opposite direction to the other. Their phase angle is 180°.
In any series circuit where the reactance is not zero the applied
emf. and the current have a difference of phase.
54. Alteznating Current in a Circuit Containing Inductance Only. —
Such a circuit would be approximately represented by one with a
large inductance coil wound with such large wire that only a very
small resistance would be offered to the current.
If an alternating emf. is applied to the circuit, an alternating
current flows, and the changes of the current induce an emf. in the
circuit which is greater, the greater the inductance and the more
RADIO COMMUNICATION.
99
rapidly the current changes; that is, the greater the frequency of
the current.
The current i changes most rapidly at the points -4, 5, and C,
Fig. 75, where it is passing through zero value. The induced emf .
must therefore be a maximum at those points. Since it always
opposes the change of ciu*rent, it must be at its maximum negative
value in the figure at the points of the axis, A and C, and at its
positive maximum at point B. At points D and E, the current does
not change for a moment, so that the induced emf. must be zero at
Cmf. *n«i currant curves with
A difference of- ^hA«« of ^5*
PlO. 13
Cmf. And owrrenT cvrvea in
V^V
FiO. 14
Twe emf. curves in o^^»ite
FlQ.15
La^^io^ curr^i^t in
(nductive circuii*
those times. It is not difficult to show that when we have a sine
alternating current there is also a sine alternating emf. induced as
shown in curve 6, Fig. 75.
In this kind of a circuit, this induced emf. has to be overcome
at each moment, but the applied emf. is not requisitioned for any
other service. Accordingly the applied and induced emfs. are at
every moment equal and opposite. The applied emf. wave is
therefore given by curve v. Fig. 75, drawn with its vertical heights
just equal and opposite to those of the curve e. It is evident that
100 RADIO COMMUNICATION.
the current lags one-quarter of a cycle in its changes behind those
of the applied emf . The current is said therefore to lag 90° in phase
behind the applied emf.
The effective value of the induced emf. can be shown to have the
value 27r/LJ, in which / is the frequency, L the inductance in
henries, I the effective value of the current in amperes, and ir=
3.1416, or nearly 3|. An effective applied emf. E^ therefore, will
produce a current whose effective value is
Inductive Reactance. — ^The quantity X—l-wfL is known as the
reactance of the inductance coil. It is larger, the greater the fre-
quency and the greater the inductance, as would be expected, and
has a considerable value in many cases. The reactance is measured
in ohms. As an example, suppose a coil of 0.1 henry at 100,000
cycles per sec. The reactance is X=6.283X 100,000X0.1 =62,830
ohms. That is, such a circuit throttles down the current as much
as a resistance of 62,830 ohms would do. There is this difference,
however, between the effects of an inductance and a resistance, that
no energy is dissipated in heat in an inductance. In one-half of the
cycle energy is taken from the circuit, it is true, but this is stored
up in the magnetic field around the coil, and in the next half cycle
the magnetic field collapses on the coil and gives the energy back
to the circuit. Thus, in the long run, energy is neither gained nor
lost in the circuit. .
55. Circuit Containing Inductance and Resistance in Series. — It is,
of course, impossible to arrange a circuit which has absolutely no
resistance. In addition to overcoming the induced emf., a portion
of the applied emf. has to be employed to force the current through
the resistance of the circuit. Thus, if the current at any moment
is passing through the value t, the emf. necessary to force the cur-
rent through the resistance is R\ and that which is overcoming the
induced emf. is Xi, so that the value e which the applied emf. has
at that moment is e^^Ii.i-\-Xi. This equation shows the simple and
obvious connection between the value of the current at any instant,
and the corresponding instantaneous value of the emf. which is
producing it. However, it cannot be used to calculate the effective
current from the effective applied voltage, for the reason that the
two emfs. Ri and Xi are not in phase. When the former is passing
through zero value, the latter is at its maximum and vice versa, so
• • •
• • • •
RADIO COMMUNIGATIOIS;.
• • «
■« I*
« It •
• • •
... i»oi
#• • • •
tf • • ••
that the sum of the two emfs. has a maxitnutir ValUte ledb' thsfti'tKe
sum of their individual maximum values.
This is in line with the results of the following experiment. Let
a coil of inductance L be joined in series with a resistance 1?, and
let three voltmeters a, 6, and c be applied, as shown, Fig. 76, to
measure the emf. between the points A and B, B and C, and A and
C. The voltages measured by the voltmeters are effective values,
and it is found that the reading of c is not equal to the sum of the
readings of a and h as would be the case with a direct current.
The voltmeter a gives the emf. RI and the voltmeter h the emf.
XI^ where I is the effective value of the current, which would be
measured by an a.c. ammeter in the circuit. Analysis shows that
^,.— ©--^,
circuit v</ith in^tueUnee an<4 iresisfiinee
75.4
V«ltd^eTn;9r^le
f-iSo l*Z L«€xl E«I6
tS6l
FiQ. -n
for circuit Kdvip^ reai'sTancc
C* loo f '^^
L -O.I f^>>io
the reading E of the voltmeter c is represented by the hypotenuse
of the right triangle whose sides are RI and XI. See Fig. 77-a.
The effective applied emf. E in such a case is therefore related
to the voltages RI and XI by the equation (relation between sides
and hypotenuse of a right triangle),
^2=(i2/)2+(X/)2= P (X2+i?2) (59)
Accordingly, the effective value of the current produced by the
effective applied emf. E is
•> ^ • C ■ ■ •
1.02 JIAPIO. COMMUNICATION.
• ••;•.• •*
* iTM)>^?lcg.— ^Thfe'qifanfity -^X^-^R^ is known as the "impedance "
of the circuit. It takes the place in alternating current theory of
the resistance in Ohm's law. It is related to the resistance and
reactance as the sides of the right triangle, Fig. 77-b.
As an example, suppose in Fig. 78 that If^O.l henry, R^IO ohms, /» 60 cycles
per second. Find what applied emf. is necessary to cause an effective current of
2 amp. to flow.
i2/=- 20 volts
X =6.283X60X0.1=37.7 ohms
X/f- 75.4 volts.
The applied emf. must therefore be by (59)
JS:=- V(20)«+(75.4)«=-78.0 volts.
The reverse problem is to find what current will flow in the circuit, when a given
emf., say 100 volts, is applied. The impedance is -y/R^+X*^ V(10)>+(37.7)»=
39 ohms.
100
Therefore the current will be 3^=2.56 amp. The emf. on the resistance is 2.56k
10=25.6 volts and that on the reactance 2.56X37.7=95.5 volts, so that the voltage
triangle is that given in Fig. 79.
Power Factor. — The power dissipated in heat in this circuit is of
course PR=(2 .66^X10^66. 6 watts. The product of the effective
current and effective voltage is 100X2.56=256 ** volt-amperes. "
To obtain the dissipated power from this product, it is therefore
65 5
necessary to multiply by 2=^-= 0.256. Note that this is the same as
39 ohms '^^® number which it is necessary to multiply into the
product of volts and amperes, in order to get the power, is called
the * ' power factor. " The power factor of the above circuit is 0.256.
A circuit with resistance only and no inductance or capacitance has
a power factor of 1. A resonant circuit (see Chap. 4) is another ex-
ample of power factor equal to 1. The power factor ia other cases
always lies between zero and one. The power in any circuit is cal-
culated, then, by the formula
P=EIF (61)
the power factor being given by the general formula
re8i8tence_
impedance ^ ^
56. Charging of a Condenser in an Alternating Current Circuit. —
A steady emf. is not able to pass a steady current through a condenser.
When the circuit is first closed, a charging current flows into the
RADIO COMMUNICATION.
103
condenser, until the voltage between the plates of the latter has
risen to the same value as the applied voltage. If the voltage is
removed and the circuit completed by a wire, a discharge current
flows out of the condenser in the opposite direction to the charging
current. The discharge ceases when the plates of the condenser
have no potential difference. (See Sec. 30.)
With an alternating emf . in the condenser circuit, an alternating
ciurent is constantly flowing into and out of the condenser to keep
the voltage between the plates equal to the instantaneous value of
the applied emf. The ciurent is largest at those moments when the
applied emf. is changing most rapidly; it is zero at the moments
when the emf. is for a moment stationary at its maximum values.
If curve €, Fig. 80, represents a sine alternating emf., it can be shown
that the charging current ciu-ve will be like curve i; that is, the
Emf. And char^iih^ cwrrwnT in cenden»«r
Current* arvel «mf!5.en co'il^nJ c«n«ien3er
-Xcl
(Xl-Xc)I
nc.&z
circuit with R,, L t^nii C
charging current is 90° ''ahead " of the applied emf. in phase. (Con-
trast this with the relations in the inductive circuit.) The charging
ciurent will, in general, be greater the greater the capacitance C,
and the greater the frequency of the emf.
Tteactance of Condenser, — Analysis shows that the effective value /
of the charging current is 7= 2TrfCE. The reactance of the condenser
is accordingly
where Cis the capacitance in farads. This shows that the reactance
of the condenser is greater, the smaller the capacitance and the lower
the frequency » (Contrast with the reactance of an inductance.)
The reactance, as before, is measured in ohms.
104 RADIO COMMUNICATION.
As an example, we find that the reactance of a condenser of 0.1
mfd. at 60 cycles is
10«
6:283X6OX0a=2^»^^ ^^°^-
At 100,000 cycles, the reactance is only 15.9 ohms. From this it
appears that the condenser offers much less obstruction to flow of
current at high frequency than at low frequency, and hence, that a
given alternating emf. causes a much larger current flow, if the
idtemations are rapid, than if they are slow.
No energy is dissipated in a perfect condenser. Energy is stored
in the dielectric of the condenser while it is being chained, but this
is all restored to the circuit when the condenser dischaiges. Actu-
ally, no condenser is perfect, although well designed air condensers
may be regarded as essentially so. Heat is always dissipated to a
measurable extent in condensers with solid dielectrics. The con-
denser acts as though a certain resistance were joined in series with
it. The actual value of this suppositious series resistance depends
upon the capacitance and the frequency, as well as upon the nature
of the dielectric. It is less, the greater the capacitance and, in
general, inversely proportional to the frequency.
57. Circuit Containing Capacitance, Inductance and Resistance
in Series. — When an inductance and capacitance are joined in series
and subjected to an alternating emf., the current through them both
is the same and the emf. on the condenser is X^i and that on the in-
ductance Xijij where the instantaneous current has the value i, X^ is
the reactance of the coil and X^ the reactance of the condenser. The
curves for these voltages may be derived by combining the curves
of Figs. 75 and 80. The curves XlI and XJi^ Fig. 81, show that
at every moment the voltage on the condenser opposes that on the
inductance. The circuit acts as though it possessed a single react-
ance equal to the difference of the reactance of the coil and the react-
ance of the condenser. If the latter is the larger, the circuit behaves
like a condenser circuit, and if the coil has the greater reactance,
the circuit behaves like an inductive circuit.
The effective values of the voltages in the circuit are shown in
Figs. 82-a and b. The impedance is found by combining the resist-
ance and the resulting impedance in the triangle diagram of Fig.
82-c. The value of the impedance is evidently
Z^^|R^->t{X^-X,Y (64)
RADIO COMMUNICATION.
105
58. Tlie Alternating-Current Transformer. — Remembering the
principles of induced currents in Section 45, it is evident that when
an alternating current is flowing in a circuit, the alternating magnetic
field will cut in and out through any neighboring circuit, and induce
an alternating emf . in the latter. This induced emf . will depend
upon the mutual inductance of the two circuits (Sec. 47) the cur-
rent in the inducing circuit, and the frequency of this current. It
can be shown that, if / is the effective value of the current, M the
mutual inductance and / the frequency, the effective value of the
emf. induced will be 2ir/i/J. In low-frequency work, M is made as
large as possible by winding the two circuits on an iron form, so that
almost all of the magnetic flux produced by the ciurent passes
through the second circuit. This arrangement is called a * 'trans-
former." (See Fig. 83.) The induced voltage is to the applied
voltage in the ratio of the number of turns on the two coils, the larger
voltage being found in the circuit which makes the greater number
ria.64
na.ea
TiVna
R/I.M'fin^ Cwrr«n1"
5im^l« Tr*rv»fermer
of turns around the iron. Thus, if one coil has 1000 turns and the
other 100, and an emf. of 200 volts is applied to the latter, an emf.
of 2000 volts is induced in the former. When current is drawn from
the second circuit, it is found that the currents in the two circuits
are nearly in the ratio of the numbers of turns, the greater ciurent
being found in the lower voltage circuit.
At radio frequencies, the effectiveness of iron in increasing the
magnetic flux is not so great as at low frequencies. (See Sec. 42,
foot-note.) To increase the mutual inductance, the coils are made
large and are brought near each other. Usually no iron core is
employed. For a further treatment, see Section 121 on coupled
circuits.
A common use of a transformer with radio frequencies is to obtain
an alternating current from a pulsating current. For example in
the use of vacuum tubes for amplifying received signals. Section 194,
Chapter 8, pulsations are produced in the plate current, above and
106 RADIO COMMUNICATION.
below its normal steady value. By passing the plate current
through the primary of a transformer, an amplified alternating emf .
is obtained in the secondary, and this emf. is applied to the grid
circuit of a second vacuum tube, and. so on. If curve a, Fig. 84,
represents a pulsating current, the latter may evidently be regarded
as compounded of a steady current (dotted line) and an alternating
current. The steady current has no inducing effect in the trans-
former, but the alternating part induces an alternating emf. in the
secondary circuit.
J. Measuring Instruments.
From what has gone before, it will be plain that the presence of an
electric current can be known by such effects as the production of
heat, magnetic action, or chemical changes. All of these effects are
greater with a strong current than with a weak one, therefore all can
be used to give an idea of the magnitude of a current. Instruments
have been invented which take advantage of each of those effects,
but some are more conveniently used than others. Those about
which the student of radio particularly needs to know are based on
two effects of the electric current; the magnetic effect and the heat-
ing effect.
Meters can be used either to indicate the current in amperes flow-
ing in a circuit, in which case they are called anmieters, or to indicate
the potential difference in volts between two points, in which case
they are voltmeters.
59. Hot Wire Instruments. — Currents of radio frequency are gen-
erally measured by means of instruments which depend on the heat-
ing of a wire or strip of metal. They are therefore called ** thermal'^
anmieters. These are again divided into two main classes, the
expansion and the thermocouple instruments. The first takes
advantage of the lengthening of a metal wire or strip when it is heated.
Fig. 85 illustrates the principle. The current to be measured
flows along the wire AB^ which is of a material having sufficient
resistance to cause it to become hot. In heating, it stretches some-
what. That permits it to be pulled aside by the spring S acting
through the thread T. The latter passes around the shaft P, and by
turning it causes the pointer to move over the scale a greater or less
distance, depending on the current in AB.^ The scale is graduated
(marked off) in amperes so that the position of the pointer shows
directly how large the current is.
1 This principle is used in meters made by the General Radio and Roller-Smith Cos.
RADIO COMMUNICATION.
107
The thermocouplfi type of ammeter * utilizes the fact that when the
junction of two dissimilar metals is heated, an emf. is developed (see
Sec. 15). A pair of metals used for this purpose is called a *' ther-
mocouple." The value of the emf. depends on the combination of
metals and ordinarily increases directly as the temperature is
increased.
In Fig. 86, the thermocouple consists of the two wires c and rf,
and their junction is in contact with the hot wire AB^ in which the
radio frequency current is flowing. The emf. produced by the
heat at the junction is applied to (r, an instrument of the type shown
in Fig. 88 below, and causes a pointer to deflect; the millivoltmeter
w/
fia.65
FIO.A6
R-inc'i^le of Ther'n**
Arn meter usi'n^ E^)Mn.ftion
Metwir*
Phi'nci^le of Thermal Ammet'er
UiSi'n^ Thermocouple
• E*
G responds to the direct current sent through it by the emf., as will
be explained in the next section.
It is to be noted that the heat due to a given number of amperes
of altematii^ current is the same as that of an equal number of
amperes, direct ciurent. In fact, an ampere is defined, in alter-
nating currents, as being such a current that the heat it produces
in a given conductor is the same as is produced by 1 amp., direct
current. (See Sec. 51.) The emf. produced at the junction does
not depend on the direction of the current in AB^ but merely on
the amount of heat produced. This emf. is always in the same
direction; it can therefore be measured by a d.c. instrument. Thus
the combination is useful for measuring high frequency currents.
The heat developed varies as the square of the current, and the
emf. of the thermocouple varies, quite closely, as the heat
1 Such instruments are made by the Weston Electrical Instrument Co. and the
Roller-Smith Co.
108 RADIO COMMUNICATION.
developed, so the indications of ammeters of the thennal type
change, practically, as the square of the current. Consequently
the scale is not uniform, being more open at the upper end than at
the lower.
In Fig. 86 the thermocouple is made to appear separate from the
rest of the instrument; in commercial anuneters the thermocouple
and the indicating instrument are placed inside the same case, and
the scale is made to read the amperes in the radio frequency circuit.
When a hot wire instrument is needed for ciurents of more than a
few amperes, it is not practicable to build it with a single heating
wire. This is true both for expansion and for the thermocouple
type. Several hot wires or strips are therefore used, arranged cylin-
drically so that the radio currents divide equally among them.
Then, either the effect on one of them alone is used to operate the
indicating mechanism, or if thermocouples are used, the emfs. of
several can be combined in series, so that their effects are added.
On some of the older radio equipments, instruments are found
which are incorrectly called wattmeters. They are, as a matter of
fact, simply ammeters in which the scale, instead of being marked in
amperes, is marked proportionally to the square of the number of
amperes. They are properly called ** current-square meters."
60. Magnetic Instruments. — While the heating effect of the cur-
rent is used for measurements at radio frequency, the magnetic
effect is the one utilized in most instruments for direct and for low
frequency alternating current. The simplest and most common
instrument for measuring direct current depends upon the force
between a permanent magnet and wire carrying current.
D. C. Milliammeter. — ^Fig. 87 represents a rectangular coil C of
fine insidated wire between the poles NS of a permanent mag-
net.* The coil consists of a number of turns wound on a light metal
frame, which is pivoted in jewel bearings like those of a watch.
SS are spiral springs resembling the hairspring of a watch, but
somewhat heavier and made of material that is a better electrical
conductor than steel. They serve the double purpose of conduct-
ing the current and controlling the position of the coil. is a cylin-
drical piece of soft iron that serves as a good magnetic path between
N and Sj and causes a strong and uniform magnetic field to exist
in the spaces between N and 0, and between and S.
1 Instruments with a movable coil in the field of a permanent magnet arc called the
"moving-coil" type.
RADIO COMMUNICATION.
109
Assume that A and B are connected to a source of emf., so that
current flows as indicated by the arrows. In the portion of the
coil next to the N pole of the magnet the current flows downward
in each turn of wire. The direction of the magnetic field is always
from N toward S, By the ** left-hand rule" (Sec. 43), it is seen
that the force on the wires is toward the front (out of the paper).
On the side of the coil near the 8 pole the current is up; that side
tends to be pushed toward the rear (into the paper). As a whole,
therefore, the coil tends to turn on its pivots. This motion is opposed
Fid 61
=o=
fVinci)>le df the Milti<»mmo1«r
Pia.8e>
FlQ.£>9
A^
R
M
R-inc'i^te «?■* Annmeter Cenn«ctron
PrinciJ>Al
and A
f DC Voltmefcr
efer
by the springs, and for each strength of current, there is some posi-
tion of the coil in which the force due to the current and the force
due to the springs balance. A pointer can therefore be attached to
the coil so as to indicate, by its position over a scale, the current
in amperes, in the coil. With the strong magnets, delicate parts,
and fine workmanship foimd in good instnmaents, it takes only a
very small fraction of an ampere to move the pointer over its entire
range; the scale may be graduated in thousandths of an ampere
110 RADIO COMMUNICATION.
and the instrument used as a ^^niilllammeter." Also, with certain
modifications to be described presently, the instrument can be
used to indicate millivolts, and is then called a "milli voltmeter.'*
The arrangement of the parts of such an instrument is shown in
Fig. 88. Attached to the ends of the permanent magnet MM are
the soft iron pole-pieces NS^ and between them is the cylindrical
soft iron core 0, mounted on supports not shown in the sketch.
This arrangement provides a strong and uniform magnetic field in
the narrow gap G. The coil C is free to turn in this gap, which is
wide enough merely to allow the necessary clearance. P is the
upper spiral spring, above the top of the coil. The other one is
under the core 0. The pointer is a thin tube of aluminuiji, flattened
at the end. The whole is inclosed in a dust tight case, with a glass
over the scale. From the description it should be evident that
abuse, such as setting the meter down with a jar, or applying exces-
sive currents, will ruin it.
Moving Coil Galvanometer, — For very delicate measurements,
where even a milliameter is not sensitive enough, the pivots and
springs are done away with and the coil is suspended by a long fine
wire or strip, which conducts the current to it and at the same time
opposes the turning effort due to the current. Another fine wire at
the bottom provides the other connection to the coil. If the sus-
pension wire is fine enough and the coil has many turns, such an
instnmaent, called a ''moving coil galvanometer," can be used to
measure currents less than a miUicnth of an ampere. No pointer is
used; a tiny mirror, attached to the coil, changes the direction of
light reflected from it as the coil turns.
Ammeters. — An instrument of the type of Fig. 88 can be built
only for small currents, otherwise the coil and other parts would be
so huge as to be unwieldy. For larger currents the scheme of Fig.
89 is used. The current in -4 is to be measured. iS is a short resistor
called a "shunt," consisting of one or several strips of a special alloy
large enough to carry the current.
The current divides, most of it going through 6', because its resist-
ance is small. A little of it flows through the milli voltmeter if, of
which the resistance is large compared with S. This current in
My though small, is a perfectly definite fraction of the total (Sec. 25);
therefore, if we know how great it is, we can know at once how great
the total is.
RADIO COMMUNICATION. Ill
For example, if the resistance of S is 0.01 ohm and that of if is
0.99, then the current divides in the same ratio, the larger part flow-
ing in the path of smaller resistance. Out of every unit of current
0.99 flows by way of S and only 0.01 passes through the millivolt-
meter. The total is 100 times as great as the current in M. If the
resistances are 0.001 and 0.999, then the total is 1000 times as great.
The small current in the meter is an accurate measure of the much
larger current in A; for any one shunt the scale is therefore made to
read directly in amperes of total current.
The number of amperes giving full scale deflection is also stamped
on the shimt. It should agree with the scale of the meter.
Instnmients of moderate range, say up to 75 amp. in one type,
may be had with the shunt built in, concealed within the case.
The binding posts are then of massive brass, with good sized holes
for attaching wires.
Aside from avoiding rough treatment, or connecting it to carry
a greater current than it is built for, the chief precaution in using
an ammeter is to connect it as shown in Fig. 89, p. 109, and not as in
Fig. 90, which connection would cause its instant destruction.
That is, the circuit is interrupted at some point and the shunt (or
the meter as a whole if it is self-contained) is inserted. If not a
self-contained instrument, the millivoltmeter should then be con-
nected to the terminals of the shunt after the latter has been
securely connected in the circuit.
Voltmeters, — ^The type of movement used in ammeters is also
used in voltmeters, but the latter are connected to the circuit in a
different way, which involves certain differences between the
instruments.
In Fig. 90, A and B represent two wires connected to the ter-
minals of a battery. It is desired to measure the difference of
potential, in volts, between them, if is a meter like that of Fig.
88 and i? is a wire of such great length and small diameter that
its resistance is sufficient to keep the current sent through the
instrument within proper limits. In one very well-known make
this resistance is around 15.000 ohms for a meter reading up to
150 volts.
The current flowing through the instrument, by Ohm's law, is
equal to the volts between A and B divided by the resistance of
R plus M, Any change in the voltage will cause an exactly pro-
portional change in the ciurent in the meter. Therefore it is pos-
112
RADIO COMMUNICATION.
sible to graduate the scale directly in volts. As a matter of fact,
for ordinary voltages, R is usually wound on thin mica cards which
occupy little space and are fastened permanently inside the case
of the instrument, out of the way of the user. He has merely to
connect one binding post of the meter to each of the two points
in question. The pointer indicates, on the scale, the voltage
between them. The main precautions to be taken in using a
voltmeter are (1) never to connect it between points of higher
FIQ.90
"t &.
to
L
Principle ef Voltmeter Cennacti«n
riQ.92
"■xa- ,
inclined Coil lype, Meter
MA^netic Vano T>^ Meter
voltage than the scale will indicate, even for an instant, and (2)
not to shake or otherwise roughly handle it.
The resistance of a voltmeter may be made sufficiently low,
without introducing serious sources of inaccuracy, to permit of its
being used to measure small fractions of one volt, in fact one stand-
ard form is made to give full scale deflection on 0.02 volt. Such
instruments are graduated in millivolts and are called "milli-
voltmeters." Even when it is used as in Fig. 89, p. 109, to measure
current, there are reasons why the instrmnent should have some
resistance besides that of the copper wire in the coil. This accounts
for the statement, made in connection with that figure, that M is
a millivoltmeter.
RADIO COMMUNICATION. 113
Ammeters and voltmeters can readily be distinguished, not only
by the marking of the scale, but by the terminals. Those of an
ammeter are large, and made to receive fairly thick wire; those of
a voltmeter are smaller, having insulating caps; the screw threads
are fine, and it is evident that they are made to receive only thin
wires, as is to be expected because a voltmeter takes a very small
current, usually less than 0.01 amp.
Other Types of Meters, — For low frequency a.c. measurements,
instruments with a permanent magnet cannot be used, and the
thermal type has not had as wide application as those types which
make use of the magnetic effect of the current on a piece of soft iron.
Fig. 91 illustrates the principle of one soft iron type. Cur-
rent flowing around the coil C magnetizes the thin iron strip F,
which is fixed in position by a stationary support. In the same
way it magnetizes the other strip if, which is movable, being
supported from the same shaft that carries the pointer P. The tope
of both strips are at any instant of the same polarity, and the bot-
tom edges of both are of the opposite polarity to this (but of the
same polarity to each other). They therefore repel each other;
the strip M moves to the right, and the pointer turns with it. The
motion is opposed by spiral springs, as in Fig. 87.
If an instrument of this type is to be used as an ammeter, the
coil is made of a few turns of large wire; if it is to be a voltmeter,
many turns of fine wire are used and a resistance R is placed in
series with the coil, inside of the case, as in Fig. 90.
It will be seen that such an instrument will respond to alter-
nating currents, for when the current reverses the magnetization
of both of the iron vanes reverses at the same time, so they con-
tinue to repel each other.
Another way of utilizing the magnetic effect is shown in Fig. 92.
The coil is inclined, and a little iron vane, also inclined, is carried
on the pointer spindle. When the pointer is held in the position
Pi by the controlling spring, the vane does not point in the direc-
tion of the axis of the coil. Current sets up a field and magnetizes
the vane which then tends to set itself along the axis of the coil,
turning the spindle in doing so, and moving the pointer against
the force of the spring to some position Pj. The difference be-
tween ammeters and voltmeters of this type is the same as in the
preceding form.
97340*'— 19 8
114 RADIO COMMTTXICATIOX.
Telephone Receiver. — The magnetic effect of the current ia utilized
in a somewhat different way in the telephone receiver. Fig. 93
ahowB, in diagram, the working parts of a "watch-case" receiver of
the kind used in radio head Beta. In the plan (h), MX ie a perma-
nent magnet, shaped like the letter C, to which are attached the
Bott iron strips terminatingin the pole pieces Nand S. Thism^netia
held in the bottom of a circular metallic cup, not shown in (5.) The
pole pieces project upward in the center of the cup as shown in the
upper figure (a), A coil of insulated wire is wound around each pole
jflece. In high grade instruments the wire is very fine and the two
4 S R
"
" 1
^
•^jQ.gs
coila contain some thousands of turns— around 10,000, roughly.
Above the pole pieces, and close to them, is a thin circular disk D of
sheet iron, called the "diaphragm." The diaphragm of a receiver
can be seen liirough the hole in the center of the hard rubber ear-
When current flows around the coila in one direction, it increases
the pull on the diaphragm due tci the permanent magnet. If it is
weakened or if it flows in the opposite direction the attraction is
lessened, A telephone current consists of pulsations in a steady
current, or, more rarely, of rapid reversals of direction.
CHAPTER 2.
DYNAMO-ELECTRIC MACHINERY.
61. Generators and Motors. — In the preceding chapter some laws
of electric and magnetic circuits are discussed, and attention is
directed to the relations between electric currents and magnetic
fields. In the present chapter certain practical applications will
be described, in which use is made of all those laws, but which are
based particularly on three experimental facts; namely, that —
1. When a conductor is moved across a magnetic field, an emf. is
induced in the conductor,
2. When a current flows in a conductor in a magnetic field, a cross-
push is exerted on the conductor.
3. When a current is sent around an iron core, the core is magnet-
ized.
The forces involved are not necessarily small, as is sometimes
imagined, but may run into hundreds or even thousands of kilograms.
Such forces can be used for power applications on a large scale, by
means of machinery, called ** dynamo-electric" or, for short, '* elec-
trical " machinery.
Electric machines are used for conversion of power from mechan-
ical to electrical form, or vice versa. If driven by some sort of
prime mover like a steam engine, gas engine, or water wheel, they
convert mechanical power into electrical power and are called
** generators.*' If supplied with ciurent and used to drive machin-
ery, vehicles, or other devices, thus converting electrical power
into mechanical power, they are called ** motors.'*
While there are various types of motors and various types of
generators, the difference is more in the use than in the construc-
tion or appearance; in fact the difference between most motors and
the corresponding kinds of generators is so slight that the same
machine can be used for both purposes with no changes, or only
minor ones. Electric machines may be built for either direct or
alternating ciurent.
A. The Alternator.
62. Production of Emf. by Bevolving Field. — It was pointed out
in Chapter 1, Section 45, that the motion of a conductor across a
magnetic field causes an electromotive force in the conductor. This
115
116
RADIO COMMUNICATION.
is true whether it is the conductor or the magnetic field that actually
moves; the essential thing is that there shall be relative motion of
one with respect to the other.
One way in which such relative motion may be secured is illus-
trated by Fig. 94. Suppose the magnet NS la made to rotate con-
r\Q.9A
Prodoe+ion of dlterf%at"rn^
"f ''y rotating m«^«t'
1
(I)
(0
7 I (5) Thew**nJRiV<>f •'W^**'^
^ I ^ 1 — \ I / ■ » ^ I ^ I • >
lo *^ I >*| ^^ ^^ ^o^
mn A;«.ii Aboot which it rev»lv««
Ab SUtionar^ loo|> <*f wire
Alternating electro motiv _
forae at r5 «iycf«a ^ar s«eon«i
iva
Fia. 96
A(tenAtir\^ omf. by multr^Ur "fisld
tinuously in a vertical plane about the axis mn. The loop of wire
ah is stationary. Its ends are connected to some external part of the
circuit, X, As the field from the N pole sweeps across a, an electro-
motive force is induced in it to the right and at the same time an
electromotive force is induced to the left in b by the passing of the S
RADIO COMMUNICATION. 117
jx)le. Thus the emf . produced tends to send a current in a clockwise
direction around the loop a6, as indicated by the arrows.
When the magnet has made half a revolution the poles have ex-
changed places with respect to a and h and the electromotive forces
are counter-clockwise around ah. As the magnet continues to be
rotated, there are thus two pulses of electromotive force (and of
current if the circuit is closed) in opposite directions for each revo-
lution of the magnet. The device described constitutes a simple
** alternating ciurent generator" or "alternator."
63. Direction of Emf. — The direction of the electromotive force,
induced in the conductor can be determined by the "right-hand
rule.'' This rule as generally stated assumes that the magnetic field
is stationary and that the conductor moves across it. The extended
thumb, forefinger and middle finger of the right hand give respec-
tively the directions of motion of the conductor, of magnetic flux,
and of the electromotive force induced.
If the magnetic field is moving, and the conductor stationary,
the rule is readily applied by recalling that the relative motion is
the essential thing. Thus in Fig. 94 the effect of having the north
l)ole move toward the reader, passing conductor a, is the same as if
the conductor were to move away from the reader, passing pole N.
64. Emi. Curve. — If the electromotive force is called positive
when to the right in a, and negative when to the left, the changes in
it may be shown by a curve like Fig. 95. Successive moments
of time are taken along the horizontal axis, and the corresponding
electromotive forces are shown by the height of the vertical ordinates.
When the north pole is in position 1, Fig. 94, no emf. is induced.
This is shown by the point marked 1, Fig. 95. A short time after*
ward, in position 2, Fig. 94, a certain maximum emf. is induced,
shown by point 2, on the curve. When the pole has moved to posi-
tion 3 the electromotive force has decreased to zero, and in position 4
it has reached a negative maximum. It then decreases again to
zero and the whole series is repeated.
A curve like the one in Fig. 95 is often called an electromotive
force curve or wave.
The emf. curves generated by commercial alternators have a
variety of shapes, but ordinarily they are not very different from
sine curves, and for reasons given in Chapter 1 are usually treated as
such.
65. Cycle, Period, Frequency. — ^A regularly recurring series of
values of electromotive force, from any point in the series to the cor-
118 RADIO COMMUNICATION.
responding point in the next series, is called a ' 'cycle. * ' The portion
of the curve in Fig. 95 from 3 to 7 represents a cycle; similarly,
the portion from 2 to 6. The time required for one cycle ib the
** period." The number of cycles per second is called the "fre-
quency."
In American commercial practice, 60 and 25 cycles per second
are the most common frequencies for alternating current circuits.
The corresponding periods are ^V and ^V of ^ second. Other fre-
quencies, for example 50 cycles, are used in Europe. For certain
purposes in radio telegraphy, 500-cycle generators are used. Quite
recently, special machines have been developed for generating
frequencies as high as 100,000 cycles per second, to be applied
directly to the radio circuits. This frequency correBix)nds of a radio
wave length of 3000 meters.^
66. Multipolar Magnets. — To produce a frequency of 60 cycles
per second by the use of a single magnet with two poles requires a
speed of rotation of 60 revolutions per second. Such a speed is not
practicable for large machines. To get 500 cycles would require
500 r.p.s., or 30,000 r.p.m. (revolutions per minute). By arranging
a number of similar north and south poles alternately, as in Fig. 96,
and providing corresponding conductors, a lower speed of rotation
may be used. As in Fig. 94, the magnet is supposed to be made to
rotate, while the conductors a, 6, c, rf, e,/ remain stationary.
When the upper north pole is coming toward the reader, electro-
motive forces v>rill be induced in the several conductors in the direc-
tion of the arrows. The conductors are all connected in series,
except between / and a, where connection is made to an external
part of the circuit, X, All are in the same relative position to the
several magnetic poles; their electromotive forces are equal, and in
the case shown, the total is six times as great as the electromotive
force in any one conductor.
For every revolution of the magnet, each conductor is passed three
times by an N and three times by an S pole. Each pair of poles gives
rise to a cycle, so for each revolution there are three cycles of emt.
in the conductors. Thus, for a given speed, the frequency is three
times as high as it would be if there were but one pair of poles.
67. Field and Armature. — The magnets {NS^ in Fig. 96, p. H6)
which produce the magnetic field of an alternator are called the "fi^ld
magnets. " If there is but one north and one south pole, the machine
1 Wave length explained in -Sec. 125.
RADIO COMMUNICATION. 119
iseaid fa>be"bipol8r;" if there are several pairs oEpolee the nuidune
ia "multipolar."
The conductors in which the electromotive forces are induced
constitute the "arroature winding." The winding is supported,
usually by being imbedded in hIoIh, well insulated, on an iron or
steel core called the "armature core." Winding and core together
Fic. ST.— WiDdings partially assembled lu a 2S-ryde syochronouB motor.
constitute the "armature," though this term is also used, loosely,
when the armature winding alone is meant.
68. CoU-Wonnd Armature. — The electromotive force developed
in one conductor of an ordinary generator is only a volt or tw6, not
enough for practical use. Armature windings, therefore, consist of
a large number of conductors, usually combined into coils (see Fig.
97) of Beveial turns each, which are pushed into slots in the face of
120 RADIO COMMDNICATION.
the armature core and then connected by soldering. The joints
b&ve to he carefully covered with tape or other insulating material.
The coils are made of copper wire covered with insulation (ummlly
cotton"! wound to the proper shape on a form, wrapped with tape,
and finally covered or impregnated with an insulating compound.
The core Blote are often lined with heavy paperof fiber. After being
placed on the core, tbe coila are held by wedges of fiber or wood
driven into the tops of the slots.
The core is built up of thin flat sheets of soft iron or eteol, ring-
shaped, with teeth on the inner edge. See Fig. 98. Enough sheets
Fia. 98,— Lamination? partly assembled, making up UUBrmatuie core otaskBlelon
are stacked up to make a cylinder of the length desired. Occa-
sionally a separator is included to provide air ducts through the
core for ventilation. The three dark rings around the core in Fig.
87 show where the ducfa ate. The teeth are carefully lined up, and
the spaces between them become the troughs or slots for the windings.
How the emf. increases and decreases in such a winding can be
studied from Pig. 99. Here the coils are drawn as if the armature
were unrolled and opened out Hat. The magnet poles are supposed
at the given instant to be over the rectangles marked N and S. Each
RADIO CX)MMUNICATION.
121
of the numbered lines in the figure may represent either a single
conductor or one side of a coil. Only a portion of the armature
winding is represented.
Imagine the poles in Fig. 99 to be moving toward the right, the
conductors 1, 2, 3, etc., remaining stationary. Starting at the instant
when a north pole is just approaching conductor 1, and a south pole
conductor 5, electromotive forces will be induced in the directions
shown by the arrows. As conductors 2 and 6, 3 and 7, etc., are
reached additional electromotive forces are induced. The maxi-
mum comes when the N pole covers 1, 2, 3 and 4, and the S pole
covers 5, 6, 7 and 8. After that the resultant electromotive force
begins to decrease, falling to zero and then beginning to increase in the
opposite direction. In this manner an alternating emf. is gotten
in which the changes occur gradually as conductors get into or out
Fia.99
" -r r
.
Te show ^^d it ion df «i«J in
ducc«eaiv* c«il«
\
C- bol« corw
5- •• slot*
of the nu^etic field one by one, or at least coil by coil. In addition
the edges of the poles are usually tapered off ("chamfered ") to make
the changes still smoother.
69. Concentrated and Distributed Windings. — Sometimes all the
turns for one pair of poles are combined into one coil, which is put
into a single pair of large slots, one for each pole. Such a winding
is a "concentrated" winding. (See Fig. 103.) When the portion
of the core imder each pole face contains a number of slots in which
the coils are placed, the winding is "distributed." (See Figs. 97,
99, 100.)
70. Magnetic Circnit. — ^It is important to get an imderstanding of
the magnetic path in an electric machine. Various shapes are
KADIO COMMUNICATION.
1. Joiima] bo:(BS.
}. Slstor winding.
S. Cabk Upa (or leads.
12. Pole shoe.
Collector rii
Field coil.
holder, with brushes.
IS, Dxistcap.
10. DiL^t washer.
20. Rotor leads.
21. Rotor lead cable tips.
22. Brush stud.
RADIO COMMUNICATION.
poeeible, but an understanding ot one makes all others easy. Fig.
100 is a diagram indicatii^ the parts of a typical magnetic circuit,
with their names. It la not intended to show details of mechan-
ical construction. The fine lines in the upper part of the figure
flhow the path of the mt^etic flux for one pair of poles. The paths
for the other poles are similar. The armature conductors are placed
in the alota as.
124
RADIO COMMUNICATION.
71. Field Excitation. — ^ThuB far nothing has been said as to how
the magnetic field is produced. While permanent magnets might
be used, they are not satisfactory for practical purposes, except in
the very little machines called "magnetos." Electromagnets are
therefore used. The poles are fitted with coils or spools of wire,
usually of a large number of turns, through which direct current is
sent from some external source.
The CO Lis are connected to a pair of metallic rings, called "slip-
rings " or collector rings, which are in contact with conducting strips,
called * ' brushes, ' ' connected to the source of current. As the entire
field structure rotates, current is brought to the coils through the
sliding contacts of the stationary brushes with the revolving slip rings.
The source of direct current is usually a separate small direct
current generator, which when used for this purpose is called an
Fia.. >ot
Produeti'en ^ Alternating errtf. hy reveWi'r^^ ceil
As - Field fr^n«t RR. -Collector rm^9
Ab- L«o^ erf wire B& - Dru^shes
''exciter." If used for one alternator alone its output will range
from 1 to 3 per cent of the rating of the alternator. When the alter-
nator is very small, like those used in the Signal Corps portable
radio sets, the exciter is larger, by comparison.
72. Stator and Botor. — ^When it is desired to refer to the station-
ary and rotating members of a dynamo-electric machine without
regard to their functions the former is called the "stator" and the
latter the "rotor."
73. Arrangement of Parts. — A good idea of the parts of a revolving-
field alternator is obtainable from the pictures in Fig. 101, which
show a complete machine, as well as views of the most important
parts. The general view shows how the parts fit together.
RADIO COMMUNICATION. 126
Through the holes in the ventilated iron frame of the stator the
outside of the core is visible. On the inside of the core the lami-
nations can be dimly seen. The two dark rings which seem to divide
the core into thirds are ventilating ducts. Where the windings lie
in the slots they are concealed by the wedges, but the ends of the
coils are in plain view. Note that the coil ends are given a twist
to make a neat construction. The four terminals at the left of the
stator indicate a two-phase machine (Section 76).
The right hand end shield shows one brush holder in place, to the
left of the bearing; the little hole to the right of the bearing is for
the stud on which the other brush holder (lying in front) is to be
mounted.
The brushes of one set slide on one collector ring, and those of the
other set on the other ring. Two brushes are used in each set, in
this particular machine, in order to have a large and reliable contact.
The ends of the cables leading to the brushes are in view on the right
of the complete generator.
On the rotor the pole shoes are noticeable, held on by six screws.
One of the connections between field coils is seen between the upper
pole shoe and the one just in front of it, near the center of the shoe.
The massive ring to which the pole cores are attached is also visible.
There are two collector rings close together, though it is a little diffi-
cult to distinguish them in the picture.
74. Other Forms of Alternator. — Thus far we have considered
alternators of which the field magnets revolve, while the armature
is stationary. That is the construction generally used on large ma-
chines, one reason being that it makes the armature easier to
insulate. But it is also possible to have the field magnets stationary
while the armature is made to revolve. Small machines are often
built this way. The principle is shown in Fig. 102.
The magnetic field occupies the space between the poles N and S
of the stationary field magnet. The turn of wire ab is made to
revolve about a horizontal axis in this magnetic field. When a is
passing under the N pole, coming toward the reader, the electro-
motive force in it is to the right, and that in b which is cutting
through the same field (the direction of the magnetic flux is from
the N pole into the S pole), but moving away from the reader is to
the left. Current will therefore flow in the turn of wire, and by
way of the collector rings and brushes in the external circuit, aa
shown by the arrows.
126
RADIO COMMUNICATION.
When the loop has made half a revolution, a is pafislng in front of
the S pole and the electromotive force in a is toward the left. In b
it is toward the right. In the external portion, -X", of the circuit the
flow of current will then be opposite in direction to the arrows.
FiQ. 103.— Circuit diagram of revolving armature alternator. A, armature; F,
frame; P, poles; R, collector rings; B, brushes; FF, terminals of field circuit;
XX, leads to external circuit.
The continued rotation of the loop thus causes an alternating cur-
rent to flow in the circuit.
The simple bipolar magnet of Fig. 102 may be replaced by a
multipolar electromagnet consisting of a massive cylindrical frame '
called the ' ' yoke, ' ' from which poles project radially inward. Direct
current is sent through coils or spools on the magnet poles. The
same kinds of windings are used for the revolving armature as are
RADIO COMMUNICATION.
127
used for the stationary kind; the only difference is that they are
put on the outside instead of on the inner face of the core.
A machine in which the field magnets are stationary, while the
conductors, in which the electromotive force is induced are rotated,
is said to be of the "revolving armature " type. A diagram of such
a machine, used in one form of radio pack set, is given in Fig. 103.^
The armature winding in this case is of the concentrated type. A
picture of a generator very much like it appears in Fig. 122.
It has previously been shown that, when the field is made to
revolve, slip-rings have to be used in the field circuit. Similarly,
when the armature is the part that revolves, there must be slip-
FlQ. lo4
Fia. los
R-odi/ction of /klterrvatj'n^ cmj by
moving iron 'Indoctbr*
Md- Poles of 3t*trondr^ «l«etrom«^nat
C,Cz«Ceras off dlUtionAr^ arrr^tvre
hU ~ Coi l« in Which ^IternAtinA •m^ u inJoc«J
11 - A^vin^ mas^e» dj iron ("loowcTorj'J
revolvec/ Ab«ut AAI4 mn.
Prodwction of C-^Kd^ae em|i.
rings in the armature circuit to provide connection with the external
portion. Such rings are shown B.t R Rin Fig. 102.
Inductor Alternator. — Another type of alternator is of especial
interest in connection with radio telegraphy. It is called the "in-
ductor alternator," and is used particularly for the generation of
continuous high frequency currents, say aroimd 100,000 cycles per
second, but is also used for lower frequencies.
The principle on which such machines operate is illustrated in
elementary form in Fig. 104. The field magnet and the armature
1 The little machine to which this diagram applies has 18 field poles and IS arma-
ture teeth, runs 3333 r.p.m., and generates current of 500 cycles frequency. It is
designed f or an output of 250 volt-amperes, to be used in a field radio pack set. The
windings are shown only ta diagram; actually the field coils average 250 turns each;
the armature coils 19 turns each. The sketch is practically to scale, exsept the col-
lector rings, which are drawn smaller so as not to conceal the armature. The whole
diameter across the frame is about 15 cm. (6 in.).
128 RADIO COMMUNICATION.
are both stationary. A considerable gap separates the armature
core from the faces of the field poles. In this gap are masses of iron,
/, free to revolve in a plane perpendicular to the plane of the paper
about the axis win. These masses of iron are called * * inductors. * * Im-
agine them made to revolve by an external force. When the induc-
tors are in the position shown, between N and C^, and S and C2 there
is a certain magnetic flux, due to the d.c. excitation. When the induc-
tors are not in that position there are long air gaps in the magnetic
circuit, which have a very much smaller x)enneability than the
iron inductors. The flux is consequently less. The increase and
decrease of magnetic flux in the coils A A sets up an alternating emf.,
because any change in the flux inclosed by a circuit sets up an emf.
in the circuit (Sec. 45) in the one direction while the flux is increasing,
and in the opposite direction while it is decreasing.
In this type of alternator, the passing of each mass or inductor
causes a complete cycle of emf., whereas with alternators of either
the revolving field or the revolving armature type it requires the
passage of two poles to cause a cycle.
75. Polyphase Alternators. — Suppose that in Fig. 94, p. 116, another
loop similar to a6, but entirely independent of it, were placed at
right angles to a6, as shown at cd in Fig. 105. The rotation of N8
would induce in the second loop an alternating emf. identical with
that in the first, having the same frequency and the same series of
values. The sole difference would be that they would reach corre-
sponding points in the cycle at different instants of time, for at the
moment when the poles were in line with the conductors of one
loop and it was having maximum emf. induced, the other loop
would have none.
Suppose the emf. wave of the first winding is given by curve I,
Fig. 106. Then curve II will represent the emf. of the other
winding. The two cm^es are first shown separately and then
combined into one diagram. They are alike in shape, showing
that the two emfs. go through the same series of values, but II is
always a quarter of a cycle behind I (see Sec. 55). Suppose the
distance 0—4 represents ^ second. Then whatever happens in I,
at any instant, happens in II just j^ second later. This is expressed
by saying that there is a '* phase difference" of a quarter cycle
between them, or that the two emfs. differ in phase by a quarter cycle.
Two emfs. which differ in phase by a quarter of a cycle are said to be
in quadrature. A generator giving such a pair of emfs. in quadrature
is called a *' two-phase" alternator. The two windings considered
RADIO COMMUNICATION.
129
separately are called "phase windings," or, somewhat loosely, the
"phases." Either one may be thought of as phase I and the other
as phase II.
It will now be plain why the pictures of Fig. 101, show four termi-
nals at the left. Two belong to one phase and two to the other.
Fi^. io6
Emf Curves -for 1 ^k\At>c circoit
X Cvryfe "jor on« ^h^ae
H C\jrw9 -jor other ^h^ae
Cwrwd -Jor f^ec-^fvise em^-
t> P»ifa>
star or Y
Fid.lOft
Three ^hase connections
There may be more than two phases, in fact, modem power-
generators usually have three phase windings.
Definitions, — ^A machine for a simple alternating current is called
a "single phase" machine. Generators used exclusively for radio
communication are generally single phase.
A machine for alternating current of two or more phases is called a
"polyphase" machine; polyphase generators are either two-phase or
97340°— 19 9
130 RADIO COMMUNICATION.
three-phase, almost without exception. They are used for power
purposes.
Arrangement of Windings. — ^An idea of the way the windings of a
polyphase generator are arranged may be obtained by referring back
to Fig. 99. Suppose another winding to be added, identical with
the one shown, •but occupying the spaces left vacant by the first
winding.* As the magnet poles move along, the windings come into
play alternately.
Notice that in a single phase generator half the surface of the
armature core has to be left vacant. In a polyphase generator, on the
contrary, the windings may cover the entire surface and usually do.
Next, suppose the two-phase windings were each made narrower,
leaving space for a third winding just as large as each of the first two.
We should then have three phase windings, and a given field pole
would pass them one after the other. Thus would be produced
three emfs. differing in phase by equal amounts.
By properly selecting the terminals, the three emfs. would
follow one another as represented in Fig. 107, and it will be seen
that now the difference between them is one-third of a cycle. In
the time of one cycle each of the three comes to a positive peak one
after the other. The emf. curves are shown in Fig. 107. The
emfs. are often spoken of as differing by 120°.
It might be expected that a three-phase machine would have six
terminals. As a matter of fact, the phases are usually so connected
in the machine that three terminals are sufiicient, as illustrated in
Fig. 108. The three coils stand for the three armature windings.
When joined as in the upper sketch, they are said to be connected
in ''delta'* when one end of each coil is brought to a common junc-
tion as atO in the middle figure they are connected in ** Y " or "star."
The lower figure is the same as the middle one, in that terminals
2, 4, 6 are all joined together and 1, 3, 5 are connected to the line-
wires -4, Bj C. By changing the position on the paper the connec-
tions are made to look simpler.
The scheme of connections is ordinarily of no interest to the
operator, except in case of trouble, and cannot be determined
without a close examination. The wires by which the connections
are made are carefully wrapped and tucked away at the end of the
1 The reader who has difficulty in imagining the second winding may trace, on
transparent paper, the winding shown and may then slide the paper to one side by
the proper amount.
RADIO COMMUNICATION. 131
armature, concealed by an overhanging part of the frame, or by the
end shield, which has to be taken off before the connections can be
traced.^
B. Alternator Theory, Losses and Efficiency.
76. Equations for Frequency and Emf. — ^The frequency of the emf .
generated by an alternator of the revolving field or revolving arma-
ture type is given by the equation:
/=^ or/=f^; (65)
•^ 2 -^ 120 ^ ^
where / = frequency in cycles per second.
p =number of poles.
n ^revolutions per second.
n''= revolutions per minute.
The passing of each pair of poles, ^ in number gives rise to one
cycle. If there are n revolutions per second, the number of cycles
per second is therefore 2 X^* '^^^ second form of the equation is
given, because the speed is commonly given in revolutions per
minute.
For example: What frequency will a 12-pole alternator give when running at
5000r.p.m.?
With 12 poles, each revolution gives 6 cycles. In a minute there will be
6X5009» 30,000 cycles. In a second there are 30,000-!-60» 500 cycles. The machine
gives 500 cycles i)er second. By the second formula we get the same answer
^ 12x5000 ^^ , ,
/— — 120~ " cycles per second.
For the inductor type the frequency is the same as the number
of inductors which pass a given point per second. Thus 40 teeth
at 25 r.p.s. give 1000 cycles per second. The inductors are usually
in the form of teeth, somewhat like gear teeth, that project from the
revolving part.
The emf. generated in an alternator depends on how much magnetic
flux is cut by the conductors per second. Increasing either the-
magnetic flux from each pole, or the number of poles that pass a
given conductor in a second, or the number of conductors connected
in series (so that the effects in them are added together) increases the
1 Discussion of this subject can be found in any textbook on alternating current
machinery. See, for example, Timbie and Higbio, First Course, pp. 114-128; Frank-
lin & Esty, Elements of Electrical Engineering, vol. 2.
132 RADIO COMMUNICATION.
emf . of the machine in a corresponding way. This may all be stated
in one equation.
E=r4>Ayh (66)
where J5= effective volts (Section 53), as shown by a voltmeter.
0=magnetic flux per pole, in maxwells or ' ' lines of magnetic
force. "
J\r= number of turns of armature winding connected in series.
/ =frequency in cycles per second.
h=a. multiplier that depends on the arrangement of the
winding and certain mathematical relations not neces-
sary to consider here.'
77. Dependence of Driving Power on Current. — ^The power con-
sumed in an electrical circuit at any instant is proportional to the
emf. and also to the current. It is therefore proportional to their
product. If the current is made to flow by means of a generator,
and if the generator is driven by an engine of some sort, the power
that has to be developed by the engine evidently depends upon the
power used in the circuit. It is worth while to trace the reason why
increased current in a generator calls for more power from the engine
that drives it.
Let the simple loop in Fig. 102 be made to rotate at constant
speed by any ** prime mover" suitably governed. This prime
mover may be anything that will make the loop go around— a man
turning a crank, a gasoline engine, a steam engine, an electric
motor, etc. At the instant when the loop is in the plane of the
paper, and a is coming toward the reader, an emf. is being induced
in it, in the direction of the arrow. If the circuit is closed, a current
flows in the same direction. But it is known (see Section 43) that
when a conductor, carrying a current, is in a magnetic field, the con-
ductor tends to move across the field. The force on the conductor is
proportional to the strength of the field and to the current. The
1 The student who has some previous knowledge of electricity will see that if 2/
poles pass a conductor per second, the average flux cut per second is 2/'X0- To
generate 1 volt requires passing 10^ lines of flux per second. Hence the average volts
per conductor are J^X^+IO*. Each turn consists of two conductors in series, so we
multiply by 2. The voltmeter reads not average but effective volts. For sine
waves the effective volts are 1 . 11 times the average, so we multiply by 1 . 11 . Collect-
2x2Xl«ll 4.44
ing all the numbers it is seen that k in the formula stands in part for — .' ^-tqs '
It also includes a factor, not greater than 1, depending on the kind of winding used,
because if the winding is distributed, the emfs. in the various turns do not rise and
fall together (there is a difference in phase), and this must also be taken into account.
RADIO COMMUNICATION. 133
direction of the force is given by the left hand rule.* Applying the
left hand rule to conductor a, it is seen that the force on it is away
from the reader, opposite to the direction in which the conductor is
being driven, so that the wire is harder to push than it would be if
there were no current. The greater the current in the Conductor,
the greater must be the force exerted to drive it around, and there-
fore the greater must be the power developed by the prime mover
in keeping up a given speed. The same reasoning applied to b shows
that it acts with a in oppK)sing rotation.
78. Losses. — Of the mechanical energy supplied to a generator
by its prime mover, not all appears in electrical form in the cir-
cuit.* Some is unavoidably transformed into heat, and thus lost for
practical purposes. The losses, which may be called power losses
or energy losses, may be classified as —
1. Mechanical losses.
2. Copper losses.
3. Core losses.
Mechanical losses are those due to friction in the bearings, friction
at the brush contacts, and friction between the air and the moving
part of the machine, commonly called windage. The latter is not
important in low speed machines, but becomes prominent in the
case of very high speed generators. Generators of the kind we are
discussing are driven at nearly consta>nt speed, so the mechanical
losses do not depend much on the load, whether large or small.
They do depend very greatly on the condition of the bearings and
brushes. Some points regarding the care of machines in this re-
spect are given at the end of this chapter, in Section 106.
Copper losses are due to the flow of current against the resistance
of the field and armature windings. They are therefore divided
into two parts, field copper loss and armature copper loss. The
former is also called "excitation loss." Since the field coils have
reiLstance (usually high) some heat is produced as the necessary
current for magnetization is made to flow through them. Like all
heat losses due to current in a conductor, the heating is propor-
tional to the square of the current, being, in watts,
W=It^Rt (67)
where 1/ is the current in amperes in the field coils and R/ is the
resistance of the whole field circuit.
1 The thumb, forefinger, and middle finger, all at right angles, giving respectively
the directions of motion, flux, and current.
134 RADIO COMMUNICATION.
To get the same terminal voltage at the armature, when the cur-
rent in the latter is large, requires more magnetization than when
the armature current is small. This in turn requires more field
current, hence the field copper loss, or excitation loss, is somewhat
greater at large loads than at small loads; that is, it varies some-
what with the load.
Like the field loss, the armature copper loss is of the PR type; it
varies as the square of the armature current, and therefore as the
square of the load on the generator. The armature resistance is
made as small as is expedient. In a large generator it may be only
a small fraction of 1 ohm, but the loss due to the great current gen-
erated will nevertheless be considerable. •
Core losseSy or losses in the magnetic circuit, are of two classes, due
to ** hysteresis" and "eddy currents." Hysteresis losses are caused
by the rapid reversals of the magnetism of the armature core. Each
molecule of the core may be regarded as a tiny magnet, and when
the magnetization of the core is changed in direction, the molecules
have to be pulled around against their mutual magnetic attractions.
It takes energy to accomplish this. In an electric machine there is
a double reversal during each cycle. This makes many reversals
per second and requires considerable power.
Eddy currents are little electric currents induced in the iron sheets
of which the armature core is made up. The thinner the sheets, the
smaller are the currents; in fact, it is because of the eddy currents
that the core has to be laminated.
Both hysteresis and eddy currents produce heat in the core, and
in producing heat they use up power which has to be furnished by
the prime mover. Therefore they are wasteful, and the designers
of electric machinery plan to keep them as small as possible.
No specific statement can be made regarding the magnitudes of
the various losses described in the preceding paragraphs, because
they depend on many factors, such as the size, the operating speed,
and special features of design. But in order to give the reader some
idea, it may be said roughly that at full load, for generators of the
usual types, the mechanical or frictional losses may range from 6
per cent for a 1-kw. machine, to 1 per cent for the 1000-kw. size;
the excitation loss, from 6 to 1 per cent; the armature resistance loss,
from 4 to 1 per cent; and the core loss from 4 to 2 per cent.
It will now be clear why the allowable power output of a generator
has a limit. Usually machines are heavy enough to give a large
margin of strength, but they cannot well be made large enough to
RADIO COMMUNICATION. 135
allow for the heat produced by severe overloads long continued.
The increased current causes heat to be produced more rapidly, and
the temperature rises. High temperature is injurious to the insu-
lation. For example, it is found that cotton should not be continu-
ously heated as hot as the boiling point of water. Cotton is the
usual insulation for the copper wires used in machinery. If the
insulation is spoiled, the current can follow other paths than those
it should, and the machine is ruined.
79. Bating; Name Plate Data. — Practically all electrical appa-
ratus, whether for alternating or for direct current generator, motor,
or other device, is designed for certain definite conditions of opera-
tion. It is standard commercial practice to attach firmly to every
electrical machine before it leaves the factory, a brass information
tag called a **name plate." This usually gives the serial number
by which the machine can be identified, tells the maker's name;
states whether the machine is a generator or a motor; what is the
maximum continuous power output; whether for direct or alternating
current; if alternating, for what frequency and how many phases; at
what speed it is to be operated; at what voltage; the maximum cur-
rent for continuous operation. Some of these items are at times
omitted, but most of them are essential. A person who wishes to
become familiar with electrical machinery should form the habit of
examining the name plate of every machine to which' he has access,
and note the differences in size, construction and use.
It has been previously said that electrical power is measured in
watts (or kilowatts, * * kw. , * ' when large) . I n a direct current circuit,
watts are the product of volts times amperes. With alternating
current something else has to be taken into account, and to get the
average power we must multiply the volts- times-amperes by the
"power factor."^ We might expect to find a.c. machines rated in
watts or kilowatts, but if we look at the name plate of a generator
we are likely to find the letters **kva." (kilovolt-amperes). That
is, instead of actual watts the permissible output is expressed as a
product of amperes times volts divided by 1000. The reason is
plain, if we remember that the whole question of what an electric
machine will stand hinges altogether on the heating.
1 Power factor is, in fact, the number by which we must multiply volt-amperes
to get true watts. (See Sec. 57.) It is commonly expressed in per cent. It cannot
be over 100 per cent and is usually less. It depends entirely on the sort of circuit
that happens to be connected to the generator, since this as well as the generator
itself controls the phase difference existing between volts and amperes.
136 RADIO COM3IUNICATION.
The heating of the field coils and armature core depends upon the
voltage generated, because that is determined by the strength of
the magnetic field, which in turn depends on the current in the
field coils. The heating of the armature conductors is determined
by the armature current; whether or not that is in phase with the
emf. makes no difference. The total heating, then, depends on the
volts and the amperes, regardless of the power output which may
be large or small, depending on the phase relation between the two.
80. Efficiency. — ^The ratio of the useful output of a device to its
input, is called its "efficiency."
In all kinds of machinery it is impossible to avoid some losses of
power, so the output is less than the input and the efficiency is less
than 100 per cent. It is lower for small electrical machines than
for large ones, and for a given machine it varies with the extent to
which the machine is loaded. Certain losses go on regardless of the
load; those are the mechanical losses, field excitation and core losses.
Others increase with the load; the armatiure copper loss rapidly,
some additional core losses and a portion of the excitation loss more
slowly. When the output is small, most of the power input is used
up in the constant losses, and the efficiency is low. With very large
outputs, the variable losses become excessive, again lowering the
efficiency. For some intermediate load, usually not far from the
rated load given on the name plate, the efficiency is a maximum.
At full load, and for the usual designs, it may range from 80 per cent
for a 1-kw. generator to 95 per cent for a 1000-kw. generator.
81. Begulation. — ^Electric generators are, with few exceptions,
intended to be operated at constant or nearly constant speed.
Assuming that the speed is constant, and that the field excitation is
also constant, the generated voltage would likewise be constant,
regardless of the current output if it were not for certain disturbing
influences. A generator operating under these conditions is often
called a ''constant potential" or ** constant voltage" machine.
The current output depends on what is going on in the external
circuit. In a city it might depend on the number of lamps turned
on. In the case of a generator supplying energy to a spark gap, it
would depend largely on the adjustment of the gap. The term
"load" is commonly used in this connection. Sometimes it means
the devices themselves, which are connected to the line, and some-
times the current taken by them. There is generally no trouble in
knowing which is meant.
RADIO COMMUNICATION. 137
Suppose we have a certain voltage generated when the load is
zero Then if the machine is made to supply current to a circuit,
the voltage at its terminals will in general be lowered, and the
greater the current, the more will the voltage be reduced. The term
by which the behavior of a generator is described in this respect is
called the ** regulation." It is found by subtracting the voltage
at full load from the voltage at no load, dividing by the full load
voltage and multiplying by 100 to get the result in per cent.
Expressed as a formula —
Regulation=(^-2^— '^ X 100 per cent.
where Fo= voltage at no load and
F,= voltage at full load.
A small percentage regulation means that the voltage remains
quite steady when the load is changed.
82. Armatnie Impedance and Armature Beaction. — There are two
reasons why the voltage of a generator is lower when it is supplying
current than when it is not supplying current, even if the speed is
entirely steady and the direct ciurent flowing around the field
maenets is the same.
(a) The armatiure windings are bound to have some resistance and
some reactance. It requires an emf. to send current through the
armature, therefore. This emf., called the armatiure impedance
drop, has to be subtracted from the emf. generated to get the emf.
left to send ciurent through the external circuit. The greater the
current, the greater the armature impedance drop, and the less the
emf. left for the external circuit.
(6) The armature winding and core constitute an electromagnet.
When current flows in the windings, the magnetic field caused by
it is combined with the magnetic field due to field strength, with
consequent decrease in armature voltage, since the resultant mag-
netic field is what determines the generated emf.
The change in the field flux by reason of the current flowing in
the armature is called "armature reaction." Armature reaction
occurs in direct current as well as in alternating current machines,
and in motors as well as generators.^
83. Effect of Power Factor on Begulation. — The reduction of ter-
minal Toltage due to the current flowing in the armature depends,
1 Swoope, p. 362; Rowland, p. 230; Franklin and Esty, Dynamos and Motors, p. 256.
138 RADIO COMMUNICATION.
not only on the magnitude of the current, but also on its phase
relation to the emf., which is indicated by the power factor. 'A
lagging current causes a greater reduction in terminal voltage than
the same number of amperes in phase, the effect increasing with
the lag. Thus at 80 per cent power factor it may be twice as great
as at 100 per cent. Conversely, a leading current, such as is taken
by condensers, improves the regulation, so that the terminal voltage
may actually be higher when current is flowing than when there is
none.
84. Effect of Speed on Begiilation. — Since the emf. is proportional
to the rate of cutting of flux, it follows that fluctuations of speed
are attended with proportional fluctuations of voltage, provided
the field excitation is not changed at the same time.
85. Voltage Control. — ^The simplest way to control the voltage
of a generator is by adjusting the strength of the magnetic field
by means of the field current. For this purpose an adjustable
resistance is inserted in the circuit of the latter, called a field
rheostat.
One kind consists of a quantity of wire of an alloy having a
comparatively high resistance, mounted on insulating supports
in a perforated iron box with a slate face, or embedded in an insu-
lating enamel. A handle is provided for making contact with any
one of a number of brass studs attached to the resistance wire at
various points, so that more or less of it can be in circuit. Ter-
minals are provided for connecting the rheostat to the field circuit.
Fig. 109 shows the principle.
The place of the field rheostat in the scheme of connections is
seen in Fig. 110, which represents the stationary armature and
revolving field of an alternator, with arrangements for supplying
current to the alternator field from the exciter J5, current being
controlled by the field rheostat R.
Small alternators for field use in radio telegraphy are often used
without a field rheostat. The voltage is kept steady enough for
practical piuT)oses by driving the machine at the right speed.
C. Direct Current Generators.
86. Commutation. — Fig. 102, page 124, illustrates the principle
used when alternating currents are generated by revolving an arma-
ture in a stationary magnetic field. But if each end of the loop is
RADIO COMMUNICATION.
139
connected to a half cylinder of metal (C, Fig. Ill), on which rests a
stationary brush B-\- or B—, than as the loop is revolved the con-
nection to the external circuit is reversed every half revolution, and
the pulsations of current are always in the same direction. The
reversing device is called a "commutator." The brushes must be
general View
Fiq.iog
PieU e.h«eslAt
DlA^Ml
LeTterd corr«s^ndl in tK« ^Wo f^^rc
~ " A~Con^cTarnn
PP- &ind ir^ bo«ts
5 S - Confa<? Stu<i9
r«A
R- Reaistanc* wTre
Sch«.mc cj- Cenneetiond of AlternAtor
E.- Ejco'iter ArmoTure. F- i^lterr\Atbr fiel«( c.eilA
K- Alternator "field rheodUt A- ■ Armature
SO set that the reversal of connections occurs at the instant when the
current in the loop is zero and about to reverse.
Thus in the figure, a is near the N pole, and if it is coming toward
the reader the emf. will be toward the right. At that instant the
current will flow out through the segment in contact with the upper
brush to the external circuit; that is, the upper brush is -|-. After
a quarter revolution the conductors will be moving along the flux
140
RADIO COMMUNICATION.
and not cutting across it, so there will be no emf . Each brush will
be just in the act of passing from one segment to the other.
After a half revolution from the position shown, b will have ex-
changed places with a. Now the emf. in h will be toward the right,
and current will flow out to the external circuit through B-\-. Thus
the same brush is always positive. In the external circuit the cur-
rent always flows in the same direction, though in the armature
conductors the current is alternating.
If an emf. curve similar to Fig. 95, p. 116, were plotted for this cir-
cuit, with time measured along the horizontal axis, and volts at any
FlO. Ill
N
=«-sr
b*-
Preduett'en oj uni-diVcotiorMkl emf. by revel vir^ coit with commulaTor
db - Revelvir^ loo|9 df wtre
> 5
C-Commut&Tbr, Two S«^m«nt5k
X - E-xternal circyit
^--.
^e^i^rcaitron o| ourrcnt.
Kle^Ative h^lf-wdvc 1 chaq^ed fo >>oaitiv« half-wAve 3
instant along the vertical axis, the result would be somewhat like
Fig. 112. Instead of a positive and a negative half wave, there
would be two positive halves, the negative being rectified by means
of the commutator.
Again, as with alternators, the need of higher emfe. than can be
developed by a single loop, and of more effective utilization of the
material, make necessary the use of coil-wound armatures and multi-
polar field magnets. With a commutator consisting of only a few
RADIO COMMUNICATION. 141
segments, say as maay eegments &b there are magnet polea, the cur-
rent would still be pulsating.
To get ft steady, practically constant emf,, commutators are used
having many segments— several hundred in the case of large gea-
erators and motors, and usually not fewer than 20 or 30 even on very
small machines for 110-volt circuits. Such a commutator consists
of bars of copper, slightly wedge-shaped, separated by thin inau-
latii^ sheets of mica, the whole assembled in the form of a cylinder
held together by strong end clamps. The segments are insulated
from the clamps by suitably shaped rings, usually of molded mica
insulation. Connections leading to the armature conductors are
soldered into slots in the segments, which commonly have li
"risers" for the purpose, extending upward at the end toward the
armature,
87. Bins *■"! Dnun Windings. — Armature windings fall into two
broad classes, called "ring" and "drum" windings, according to
the way the conductors are mounted on the core. In the first of
these the wire is laid on the outside and passed through the hollow
Space inside of the core, being threaded through and through much
as a napkin ring or a bridle ring might be covered with string.
Ring windings are scarcely ever used nowadays. Modem ma-
chines have windings of the type shown in Fig. 113, called "drum"
142 RADIO COMMUNICATION.
windings. The conductors are all on the outer face of the core,
and the two branches of a turn lie under adjacent poles, of oppo-
site polarity. These two features are characteristic of all kinds of
drum winding. In the kind illustrated in the diagram, starting
with commutator segment 1, we pass up to conductor 6, which at
the instant shown is under a S pole. It is connected at the back
of the armature to t, which lies under a N pole and is soldered into
segment 2. Starting at 2, we have d under the edge of the S pole
back-connected to k under the edge of the N pole; k is attached to
segment 3. Continuing in the same way all around the armature
we finally have 16 loops connected to the 16 commutator segments.
It will be understood that an actual machine has a great many more
turns in the armature winding and a larger number of commutator
segments.
At the four segments marked -|- or — , contact is made with brushes
leading to the external circuit. By the ' 'right-hand rule " the emf .
in conductors under the N pole is toward the back end, so current
flows into the armature at segment 3. The brush on that segment
is therefore negative. The brush at segment 7 is positive, because
there the current flows out of the armature. Similar reasoning
applied to the conductors under the S poles leads to the same result
as to polarity of the brushes, which are thus seen to be alternately,
one positive and the next negative, as we go around the commutator.
If a machine having more than two sets of brushes is examined it
will be found that all the positive brushes are joined by a heavy-
conductor and all the negative brushes by another. Then one con-
nection is made from the group of positive brushes to the external
circuit, and one from all the negative brushes.
In speaking of alternators, the actual construction of armatures
was described ; that is, the use of machine-wound coils in slots in the
face of a laminated core. D.c. armatures are made the same way
except that the ends of the coils are soldered to the commutator
segments.^
The main steps are shown in Figs. 114, 115, and 116. The first
shows the copper segments, with their sheets of mica between them^
assembled in the form of a ring and held together by a firm tem-
porary clamp. The next picture shows the commutator fastened on
the front end of the armature core. The ''risers" are to be seen
1 Brief information on the care of commutators and proper position of brushes is
given at the end of this chapter in Sec. 106 on * 'Common troubles. "
Flo. 114. — (Upper) Msthod ot aasenibling commutator segmenls.
(Ulddle) Commulator and armsture core HsiembLed sbowing rl^cs
(Lotrer) Anualure completB wltli windings connected to risers.
144
RADIO COMMXTXICATIOX.
coming up from the ends of the segments for connection to the arma-
ture ooil«. On the core, built up of thin laminationn, note the teeth,
filot0, and three rows of air ducts for ventihition. The hist picture
shows the coils in the slots of the core. Their ends have been bo1>
dered to the commutator.
SS. Excitation: Separate, Series, Slmiit, Convoiuid.— While alter-
nat//r» rer|uire d,c. from a separate source for their field excitation,
dhef:i current dynamos excite their own fields. Depending on the
scheme of connections between the armature and the field coils, this
/
HO
.S«^r*fo
Fia. 117
V^riews n*o<le3 of
A •Armature
F- Fine w/'me orshufit-
5 -Series f^U
winolir\A
^hunT
giveH riwe to several arrangements, all of which are of practical im-
portance. In this discussion we leave out of consideration the
* 'magneto", which depends for its magnetic field on a group of
permanent magnets.
Fig. 117 shows the several ways of exciting the field magnets,
and incidentally illustrates the conventional symbols generally used
for an armature and for field windings. In this sort of diagram no
atU.'mpt is made to draw a picture of the machine. A whole set of
RADIO COMMUNICATION. 145
field coils, for example, is represented by a single coil, the armature
and brushes by a single circle^ and two strokes.
Ssparate. — The first sketch indicates that current for the field coils
comes from a source, like a battery, entirely independent of the
armature. Such a machine is said to be * 'separately excited.'*
Shunt. — The next indicates that the current from the armature
divides; some goes to the load circuit, some to the field coils; the two
unite again and flow back into the armature at the brush of opposite
polarity. When the current from the armature divides, a portion
flowing through the field winding, the machine is spoken of as a
' 'shunt generator. " Only a small fraction of the total current which
a machine is able to generate continuously is required for shunt field
excitation; it may be 5 or 6 per cent for a 1-kw. generator, and as
little as perhaps 2 per cent for a 100-kw. generator.
• Shunt field windings consist of many turns of fine wire (insulated,
of course). There may readily be 2000 or 3000 turns. For in-
stance, the little exciter for the 500-cycle audio frequency generator
described on p. 152, is a direct current shunt generator. Each of its
two field coils has 2800 turns of wire about 0.25 mm. (0.01 in.) in
diameter. Using this great quantity of fine wire has two conse-
quences; because of its high resistance it lets only a small current
flow; because of the large number of turns this small current suflices
to produce the desired magnetomotive force (which depends on the
*' ampere turns").
SerieH. — When the whole current from the armature flows through
the field coils, the generator is ** series excited." Two ways of repre-
senting a series generator are shown in Fig. 117. Heavy wire is
used for series coils. They have to carry the full current output of
the machine; fine wires would overheat and destroy the insulation.
The necessary ampere turns are secured by virtue of having a large
number of amperes and comparatively few tiu*ns of wire.
Compound. — When a generator is provided with two sets of field
coils, one of fine wire connected in shunt and the other of a few turns
of heavy conductor connected in series with the armature, it is called
a ''compound wound*' generator, or more commonly just a "com-
pound" generator. Two ways of representing it are shown in
Fig. 117.
1 Note difference from alternator, which has two circles, representing slip rings.
97340°— 19 10
146 RADIO COMMUNICATION.
89. Characteristics of Terminal Voltage. — ^Why aj^ so many
different kinds of connection used for field excitation? Ordinarily
the load on a generator will vary. By this we mean that there are
changes in the number of devices switched on; lamps may be
. turned on or off, or motors started and stopped. Such changes of
load automatically affect the terminal voltage of the generator, but
they affect it differently, according to the kind of field excitation
used.
To see why the effects differ, in each case consider the dynamo
driven at a steady speed without load. Then imagine the load (cur-
rent through th^ armature) to be successively increased. If sepa-
rate excitation is used, a certain emf . is generated at no load. When
current flows in the armature, some of this emf. is used up in sending
the current through the resistance of the armature itself. There is
also another effect, due to "armature reaction,'* * which weakens the.
magnetic field. Both increase as the armature current increases,
rience the terminal volts are less when the armature current is large,
than when it is small. Curve a. Fig. 118, shows this graphically.
The load current in amperes is plotted along the horizontal axis,
the terminal volts along the vertical axis. The greater the cmrent,
the lower the voltage. The difference between no load and full
voltage shown in the diagram corresponds to a regulation ^ of some
8 per cent, and applies to rather large machines, say of 100 kw. or
more. For a smaller one, the difference would be greater.
When shunt excitation is used the reduced terminal voltage sends
a reduced current through the field coils, so the magnetic flux is
weaker, the greater the armature current. Hence the terminal
voltage falls off more than it does with separate excitation. Thus
ciu-ve 6, Fig. 118, droops more than curve a. The dashed part
shows how the voltage falls off when the machine is greatly over-
loaded.
With series excitation, the condition is very different. When no
current flows, only the weak residual magnetism of the iron is avail-
able, and the emf. generated is consequently very small. Curve c
shows it by starting only a very little above the zero value. If
current is taken from the machine, this current, flowing in the field
1 Armature reaction is explained in Section 82 and aho in Franklin and Esty's
Elem. of E. E., vol. l,p. 151; Franklin and Esty, Djniamos and Motors, p. 176; Timbie
and Higbie, Direct and Alternating Currents.
« Defined in Section 81.
RADIO COMMUNICATION.
147
coils, strens^hens the magnetic field and so causes a greater emf . to
be generated. The greater the current taken by the external cir-
cuit, the greater will be the voltage. Hence curve c rises.
In the compound generator the two effects are combined. De-
pending on the relative proportions of the two windings, the voltage
at full load may be made equal to that at no load, or greater, or less;
the latter is rare. C'lurve rf, Fig. 118, is for a generator somewhat
J3
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"over-compounded.*' If the full load voltage were the same as the
no load voltage, the generator would be "flat-compounded."
In examining a generator, it is usually impossible to determine
whether the field coils are of fine or thick wire without tearing them
open, because they are protected with wrappings of tape, hard cord,
or other covering. To distinguish between shunt and series coils is,
however, quite easy by looking at the connections. Those between
the shunt field coils on the different poles are small because they
have to carry only a small current, those between the series coils are
148 RADIO COMMUXICATIOX.
heavy, consisting of thick, wide straps of copper on the larj»er gener-
ators.
90. Smf. SqiiAtion. — It has been stated that the emf . developed
in a conductor depends on the rate of cutting the magnetic flux *
and is equal in volts to the number of magnetic lines of force cut per
second, divided by 10*. On an armature a number of such con-
ductors are connected in series and their emfs. are therefore added.
Thus in Fig. 113, the conductors which would have to be traversed
in going from one brush on the commutator to the next through the
armature constitute one such group. There are three other similar
paths, and these four paths are all in parallel, so the resulting emf.
is the same as that of one path alone, but the current that goes to the
external circuit is the sum of the currents in the four paths.
Let N=the number of conductors in series.
n=number of revolutions per second (not per minute) of the
armature.
p=number of magnetic poles.
0=magnetic flux per pole.
Then the flux cut per second by any conductor is nXpX<l> lines.
Dividing by 10^ gives the average volts. If there are JV^ conductors
in series, the total emf. is
^This formula shows that the voltage of a generator can be changed
by changing the speed n, the flux </>, the number of poles p, or the
number of conductors N. The last two, of course, are fixed once for
all when the machine is built; the first two can be changed quickly
by the operator, and afford practical means of controlling the voltage.
This formula means exactly the same thing as the one given for
induced emf. in Chapter 1, namely that E=^~r-' It is merely nec-
essary to note that if nXp poles are passed per second, then the time
required to cut the flux 4> is only th of a second; this takes the
place of t in the denominator; or what amounts to the same thing as
dividing by —r-r-, we multiply by nX/>. The reason for the factor
10^ in the denominator has been explained.
1 Chapter 1, Section 45.
RADIO COMMUNICATION. 149
91. Voltage Control. — The practical way of controlling the voltage
of separately excited, shunt and compound generators is by having
an adjustable resistance, called a "field rheostat" (Fig. 109), in cir-
cuit with the fine wire (shunt field) coils. The points R in Fig.
117, show where such a rheostat might be put in the circuit of each
machine.
92. Effect of Varsring Speed. — ^A rise or fall of speed causes the
emf . of a separately excited generator to rise or fall in about the same
proportion. In shunt and compound generators the effect is greater.
That is why engines for driving such generators have to have good
governors, if a steady voltage is wanted.
Because of these characteristics, each type of generator has its
special uses. For instance, the exciter for the a.c. generator of a
radio field set is a simple shunt generator, because the load does not
change much. The shunt generator is good also for charging storage
batteries. Incandescent lamps need a very steady voltage that is
not changed when some of them are turned on or off. A compound
generator meets this requirement.
D. Special Alternators for Radio Use.
93. Audio Frequency and Radio Frequency. — ^Alternating cur-
rents are generated at various frequencies, covering a remarkably
wide range. Depending on their application, the frequencies in
practical use fall into three well defined classes:
(a) Commercial frequencies, which nowadays generally mean 25
or 60 cycles per second.
(b) Audio frequencies, around 500 to 1000 cycles per second.
(c) Radio frequencies, usually between 100,000 and 1,000,000,
but extending in extreme cases down to perhaps 10,000 and up to
several million cycles per second.
Commercial frequencies are used for lighting and power. The
great machines in the central stations which supply our cities with
current operate at these frequencies.
Audio frequencies are those conveniently heard in the telephone.
When alternating currents are sent through a telephone, the dia-
phragm of the latter vibrates. The vibrations are heard as sound.
The more rapid the vibrations, the shriller the tone. Vibrations at
the rate of 4000 or 5000 per second give a shrill whistle, while the
lowest notes of a bass voice have somewhat under 100. If a 500-
cycle generator supplies current to a spark gap and the spark jumps
150 RADIO COMMUNICATION.
once on the positive and once on the negative half -wave, then at
the receiving station, the signal is heard in the telephone as a
musical tone of 1000 vibrations per second.
Radio frequencies occur in the circuits of radio apparatus, for
instance in an antenna. They are too rapid to cause a sound, in a
telephone, which can be heard by the human ear. They may be
generated by dynamo-electric machines of highly specialized con-
struction, but are usually produced by other means.
94. Audio Frequency Generators. — ^To show how the methods
described in the preceding sections are applied in actual generators,
a few typical machines, used in radio sets, will be briefly descibed.
Whether or not these are of the latest design is not important.
Changes of detail are constantly being made, but they do not affect
the principles used and can be readily understood after the workings
of similar machines have been grasped. The examples of machines
here given will also illustrate how the form of generator and the
auxiliaries used with it are influenced by the source of power avail-
able for driving it.
The generator is only one part of a unit for converting energy into
the electrical form. The other part depends on the source of energy
available; it may be heat derived from coal or gasoline; it may be
falling water, moving air, human muscles, or a chaiged storage bat-
tery.
Crank Driven. — ^The field radio pack set furnishes an example of
a self-contained generating unit driven by hand. These sets have
been changed somewhat from time to time and can therefore be
described only in a general way. The generator is cylindrical in
shape and is entirely incased, including the ends, in a metal shell.
At one end of it is a flywheel for equalizing the speed. At the other
is the train of gears, running in oil and inclosed in a housing,
through which power is transmitted from the crank shaft to the
generator shaft. The crank shaft is turned by means of a pair of
cranks.
The alternator is a 250-watt, 500-cycle machine of the revolving
armature type. The exciter ^ is built in with the alternator, so that
the two have but one frame and one set of bearings, and the same
shaft carries both armatiures. Near one end, on opposite sides of
the shell, is a pair of holes giving access to the d.c. brushes which
bear on the commutator of the exciter ^ and near the other end are
1 A little generator of d . c. for the fixed coils of the alternator. See Sec. 71.
s The commutator is described in Sec. 86.
RADIO COMMUNICATION.
151
similar holes for the a.c. brushes that bear on the collector rings.
The crank is turned at the rate of 33 to 50 r.p.m., depending on the
machine (that is, the date of the model), and the generators make
3300 to 5000 r.p.m., the cranks being geared to them at a ratio of 1
to 100.
The diagram and data of Fig. 103 apply to the alternator of such
a set, the armature having 18 teeth, the same as the number of field
ni
FI0.1J9
ConneeTi'ona of ^<»cK5et'
^ervardToP
D - exciter Armature
LP - txciter field
AF- AlteroAlbr -field
Pi Pjf "Ptf^ conneotfona
K - ^•ndin^ Key
T - Coil of trdknsformer
Soo cyele A.C.
E.x.ft«ld rheo.
Qen.'fi«ld rheo
Ejiciter
3e^nt|>
dien«n4lop
CStfhemA of connection of di Tractor set ^<en«rdiTor
And eXeiter
poles. To get 500 cycles it must make 3333 r.p.m., which corre-
sponds to a crank speed of about 33 r.p.m.
The connections are shown in Fig. 119. The field coils of the
exciter are connected directly to the brushes. The circuit to the
alternator field coils passes through a receptacle Pi on the side of the
machine. A two-wire cable can be plugged in at this point, for the
sending key. While the key is closed, field current flows and a.c. is
152 RADIO COMMirXICATIOX.
generated in the annatuie. Another receptacle P, provides for
connecting the alternator armature to the transformer from which
current is supplied for the spark.
In view of the hig^ speed at which these generators run (some
make 5000 r.p.m.) the brushes have to fit very smoothly and the
bearing surfaces, particularly the d.c. conmiutator, have to be in
good condition. For ease of turning, they should not be pressed in
harder than necessary; on the other hand, unless the contact is good,
the set fails to operate satisfactorily. The most conmion troubles,
electrically, are due to a dirty conmiutator, poor brush contacts, or
to tiuning the brushes in replacing them, so that the curve of the
brush does not match the curve of the commutator.
Gasoline Engine Driven. — ^Hand power is not practical, except
for very small generators, since a man can develop only about one-
tenth of a horsepower if he has to keep it up for more than a short
time. One of the most convenient sources of larger power is the
gasoline engine. It is particularly suitable for isolated stations, or
for the more powerful portable sets, like the field radio tractor sets.
Detailed information about any particular set is supposed to be
furnished with the set, but certain features are likely to be common
U) all.
The speed of rotation of the alternator, is almost alwa3rB much
higher than that of an engine; it is therefore stepped up by pulleys
and belts, or sprockets and chain, or gears, the smaller pulley or
sprocket or gear being on the generator shaft.
The generator may be of any of the three possible types previously
described; for example, one of the permanent Signal Corps stations
uses an inductor alternator (Sec. 74); one kind of tractor set also
has the inductor type; another has the revolving armature. If it
becomes necessary to open the machine, it is easy to discover which
type it is. If the rotor, or revolving part, has no windings at all,
then we are dealing with an inductor alternator; if the circuit lead-
ing to the transmitting apparatus (not necessarily the key, be-
cause that may be in the field circuit) comes from the slip rings,
then the revolving part must be the armature.
In one of the sets of this latter type the alternator and its exciter
are two separate machines, connected by a coupling so that both
revolve together. A frequency indicator in front of the chauffeur
guides him in controlling the speed of the engine so as to maintain
the right frequency — 500 cycles per second. The combination is
chain driven from the main transmission. The same engine that
RADIO COMMUNICATION. 153
drives the truck is used to furnish power for the generator, the one
or the other being thrown in as desired.
The following name plate data of this particular set will illustrate
some of the statements made in earlier sections:
Generator frequency, 500 cycles; poles, 30; kva., 2.5; open cir-
cuit volts, 245; loaded key volts, 110; 2kw. atO.SOp.f.; 2000 r.p.m.
Exciter, shunt type: poles, 2; load volts, 110; load amperes, 2.7;
0.3 kw.
From the speed, 2,000 r.p.m., and the stated number of poles,
30, each revolution gives 15 cycles and the cycles per second will be
15X2,000/60=500, which checks with the figure given.
From the loaded key volts, 110, and the rating, 2.5 kilovolt-am-
peres or 2500 volt-amperes, the full load current is 2500/110 or 22.7 am-
peres. The product of volts, amperes, and power factor gives power
in watts; thus 110X22.7X0.80=2000 watts, or 2 kw. The great
difference between the volts on open circuit, 245, and volts when
loaded, 110, shows that the armature has a high impedance. It
must not be assumed that this loss of voltage is all due to resistance,
and so represents a waste of power. Much of it is due rather to the
demagnetizing action mentioned in Section 82, which causes a reduc-
tion in the effective magnetism and therefore in the emf . generated.
The scheme of connections in Fig. 120 shows that the exciter
voltage can be controlled by means of the exciter field rheostat. This,
in itself, would govern the 500-cycle voltage fairly well, but a
second control is provided in the generator field rheostat. High-
resistance connections between each machine and the ground pro-
vide a leakage path for high voltage charges and prevent their
accumulation.
Fan Driven. — ^Audio frequency generators have an important
application in furnishing current for communicating from airplanes.
Fan motors have been used as a source of power, though it has been
objected that they increase the head resistance of the plane. There
is no theoretical reason why any type of self-contained generator
might not be used, but because of the high rotative speeds obtainable
with fans and the need of lightness, special machines have been
developed with the fan mounted directly on an extension of the
shaft. One very recent form is described on page 159.
Motor Driven^ by A.C. Motor. — ^When electric current is to be
had, but not at the desired frequency, use may be made of a com-
bination of a motor, adapted to the circuit that is available, and a
500-cycle generator. Such a combintion is called a ' 'motor-generator
154 KADIO rOMMDXICATION.
set." For use with lio-volt, 60-cycle alternating current, sets me
built using the same sort of generator (vrith bull t-in exciter) described
in connection with hand driven apparatus. Mounted o
4 polF3 on Etator;
2. Collector rings, 1. Shaft ot both units.
bedplate with it is an a.c. motor. The shafts arc connected by a
flexible coupling.
Except for tbe mechanical connection between the shafts, the two
machines are entirely independent. Electrically there is no connec-
tion. The motor ia designed to run automatically, at the proper
speed tor the generator, or perhaps it would be better to say that there
are certain definite speeds at which 60-cycle a.c. motors have to
156
RADIO COM3IUNICATION.
run, and the generator has such a number of poles that it gives the
desired frequency when driven by a motor operating at one of these
speeds. Voltage control of the generator is secured by means similar
to those shown in Fig. 120.
Motor Driven by D.C. Motor, — ^When direct current at 110 volts is
available, the arrangement is somewhat different. The exciter is
unnecessary, because current for the field coil of the alternator may
be taken directly from the line. It is then possible to combine the
generator and a 110-volt, direct current, shunt motor (see Sea 97)
FlQ 1T3
Cohn«cti"on« o|- melbr -^ener^lor for conversion -fpom QC. to A-C
M- Motor ArmaTure E, - Motor f lalol rKeoatAt
O - Cjenerater armature ^7 - Oenorator field rKeodlAf
3.B1 — Motor Al<»rTif\^ boA
OF - Oener^ter f leicf winding
into a very compact unit. The two armatures are on the same shaft
and the two frames are joined in one structure.
Fig. 121 represents such a unit, which is shown partly disas-
sembled in Fig. 122. The generator happens to be of the same
design as that shown in diagram in Fig. 103, but being built for
nearly 50 per cent more power, it is spmewhat larger, has more poles, .
and runs at a correspondingly lower speed to give the same fre-
quency. The two armatures are seen on their common shaft; the
collector rings are near one end and the commutator near the other.
One scheme of connections for such a unit is seen in Fig. 123,
which shows the d.c. motor connected to its line by way of a switch
RADIO COMMUNICATION.
157
and starting box.* The rheostat shown in circuit with the motor
field may be omitted. Its purpose is to give control of the motor
speed, ^ if such control is desired, in order to get some definite fre-
quency quite accurately in the a.c. circuit. From the d.c. line,
connection is made also to the generator field winding, the flow of
current being controlled by another rheostat which determines the
magnetization and therefore the generator voltage. Thus the gen-
erator frequency may be governed by means of the motor field
rheostat and the voltage by the generator field rheostat.
Motor Driven Indttctor Alternators. — ^Thus far in this part of the
chapter, attention has been centered on revolving armature gener-
ators. It is equally feasible to generate 500-cycle current by means
of inductor alternators. Fig. 124 represents a motor-driven in-
ductor alternator for conversion from direct to alternating current
at 500 cycles. The table following gives the data as taken from
the name plate.
Name plate data for motor-generator shown in Fig. 124.
Volts
Amperes
Revolutions per minute
Rating
Shunt field amperes
Cycles per second
D.C. motor.
120
7.3
2500
lh.p.
0.4
A.C. gener-
ator.
125
5
2500
0. 625 kva.
500
Here again the two distinct machines, motor and generator, are
combined in a single compact unit. The armatures are on one shaft
and the two frames are made into one structure, though openings
are left for ventilatibn. These, as well as other openings at the
ends of the machine, are screened to keep out foreign material,
while permitting a free flow of air for cooling. The generator frame
is cast in the form of a cylindrical shell. At each end is inserted
a laminated armature core, with teeth projecting radially inward,
on which the armatmre winding is placed. Between the two arma-
» Described in Sec. 97.
*How this is done is explained in Sec. 97.
Fio. IM.— Inductor alttniator type inotor-genBrator se
2. Generator urmatun coiis, second 5. Inductor teeth.
3. Oeneroto tteld coU. 7. D.c. motor unuti
RADIO COMMUNICATION. 159
ture cores is the field winding, a single large coil which fits inside
the cylindrical shell where it is rigidly held in place. This coil
produces a magnetic flux parallel with the shaft. The armature
winding is in two groups, one on each core. Each group consists
of 12 coils, and the coils are all connected in series.
The portion of the set so far described is stationary. The rotor
is a solid cylindrical core, at each end of which is a ring of 12 teeth
projecting radially outward. The core is magnetized by the sta-
tionary field winding previously mentioned. To trace the mag-
netic circuit, begin at the core. One end of it is N, the other S.
The flux passes out through all the rotor teeth at the N end, across
the air gaps, into the adjacent stator teeth, through the corresponding
gap into the rotor teeth at the S end, and thence into the central
core again. As the rotor is made to revolve, the teeth are alter-
nately in line with the armature coils then opposite the spaces
between coils. The flux through the coils consequently pulsates,
and alternating emfs. are induced.
So far as the diagram of connections is concerned, Fig. 123 applies
to this case quite as well as to the preceding one, for the shunt
motor and generator field are supplied with direct current in either
event, and alternating current flows from the alternator armature,
whether that be revolving or stationary.
Self Excited Inductor Alternator, — A very novel construction has
lately been worked out for fan drive on airplanes. A simplified dia-
gram of it is given in Fig. 125, from which the electrical and mag-
netic circuits may be traced, and the principle of its operation may
be followed. For the moment, ignore the windings on the rotor.
The machine is then seen to be an inductor alternator. The a.c.
winding is on the 16 stator teeth, each tooth and its adjacent slot
spanning 1/24 of the circumference. These teeth, in groups of 4..
form four polar projections.
The polar projections are made to have opposite polarities around
the stator, so that there are two N and two S poles, by means of direct
current sent through the field coils F, each of which consist of a large
number of turns. The field coils are all connected in series to the
source of direct current, to be mentioned hereafter, but the connect-
tions are omitted from the sketch to avoid having so many lines.
When the rotor is made to revolve, the flux through the stator
teeth pulsates, and alternating emfs. are induced in the coils encir-
160
RADIO COMMUNICATION.
cling them. By symmetry, whatever happens in any one coil is also
going on at the same time in eleven others. The passage of the in-
ductor across a pair of consecutive, oppositely wound teeth gives
rise to one cycle. The generator here represented is intended for
Fig. 125.— Self-excited inductor type alternator. (4.500 r. p. m.; 75 volts; 5 amp..
900 cycles per second.) A, terminals of a. c. winding; B, brushes for taking d. c;
from commutator; C, commutator segments; F, d. c. field coils; J, inductors;
T, stator teeth.
operation at 4500 r.p.m. and at that speed, with the 12 inductors as
shown, gives a frequency of 900 cycles per second.
Besides having on it the inductors for the alternator, the rotor also
functions as a d.c. armature. That accounts for the windings shown
RADIO COMMUNICATION. 161
on the rotor. How such an armature generates direct currents is
explained in Section 87. For present purposes it suffices to say that
the armature consists of a large number of turns, wound of course for
four poles; each turn spans three teeth. In the diagram the con-
nections have been simplified for purposes of illustration, and the
number of commutator segments shown is much smaller than on the
actual machine. Connections not shown in the figure, are made
between the field coils and the four brushes, two positive and two
negative. The brushes are shown in the diagram on the inside of the
commutator, for clearness; actually they are on the outside. The
direct current from this armature is what energizes the field coils.
It will thus be seen that the rotor serves two entirely distinct
purposes:
1. It carries the inductors for the a.c. generator, which has sta-
tionary field and armature coils.
2. It carries the d.c. armature which corresponds to the exciter in
other machines.
95. Badio Frequency Generators. Alezanderson High Frequency
Alternator. — Frequencies as high as 100,000 cycles per second have
been secured by a special form of alternator * of the inductor type. It
can be seen at once that 100,000 inductor teeth have to pass a given
point every second. This extraordinary number can be obtained
only by having a great many teeth on the rotor and driving it at an
unusually high velocity besides. In a 2-kw. generator, the rotor has
300 inductors and makes 20,000 r.p.m. which gives the required
6,000,000 inductors per minute. With a rotor about 30 cm. (1 ft.)
in diameter this allows 0.3 cm. (i in.) for each slot and tooth to-
gether, and even then the rim travels something like 19 km. (12
miles) a minute. The armature conductors ar^ laid zigzag in little
slots in the flat face of the core, this face being perpendicular to
the shaft. (See Fig. 126.)
The rotor consists of a steel disk with a thin rim and much thicker
hub, shaped for maximum strength. Instead of having teeth on the
edge, it is slotted with little windows, the inductors in the form of
spokes, and leaving a solid rim of steel. Then to cut down the air
I Developed by E. F. W. Alexanderson, of the General Electric Co., U. S. Pats.
1,008^77; 1,110,028. Description of several models is given in Goldsmith's Radio
Telephony, beginning at p. 117. See also G. E. Review, vol. 16, p. 16 (1913).
97340*'— 19 11
1G2
RADIO COMMUNICATION.
friction, the slotfi are filled with non-magnetic material such as phos-
phor-bronze, finished off smoothly with the face of the disk. These
machines embody a number of novel features made necessary by the
small space per inductor and the exceptional speed. Their construc-
tion became possible only through engineering skill of a very high
order and by fine workmanship. They are not suitable for field
Winding ,sch« me cff AlexAnderdon /llternAter
d-^l*t» in roTer
FiQ.i^i
■^OTOOtXT^
C|
^7
^B
dt^ter
Circuits of
C]oldschmidt Alternator
use, however, and for that reason a detailed description is not given
here.
Goldachmidi Alternator, — ^A principle not previously mentioned in
connection with electrical machinery is utilized in the generators
of certain high power German stations. Advantage is taken of the
building up of large currents by electrical resonance (see Sec. 109) in
RADIO COMMUNICATION. 163
the rotor and stator circuits of the machine itself, as well as of the
multiplication of frequency by the effect of rotor currents on the
stator windings.*
Without undertaking to give the proof here, it may be stated
that when a rotor is revolved, and at the same time alternating
currents are made to flow at a frequency corresponding to the speed
of rotation and to the number of poles, then, due to these currents,
pulsations take place in the strength of the magnetic field of the
machine at double the frequency of the alternating currents.
The circuits (in simplified form) are shown in Fig. 127. Imagine
S to be the stator winding, energized by some source of direct
current, such ag a battery, B. In the magnetic field due to the
stator there is revolved a rotor, represented by the coil R. Suppose
it Is revolved at such a speed that the alternating emf. induced in R
has a frequency of 10,000 cycles per second. By way of the slip
rin':j3 this emf. is impressed on the circuit C^L2C^, which is tuned
(Section 110), so that, when the inductance of R is taken into ac-
count the natural frequency is the same as that of the emf. Then
heavy currents will flow in the rotor.
According to the statement made above, pulsations will take
place in the magnetic flux at the rate of 20,000 per second. These
will induce a 20,000-cycle emf. in 8. If the inductances and capaci-
tances SC^L^C^ are chosen for resonance at that frequency, large
currents will flow in the stator at the same time with the steady
current from the battery. These high frequency currents are pre-
vented from flowing through the battery by the high inductance L.
The 20,000-cycle stator currents cause a 20,000-cycle pulsation
of the magnetic flux in which the rotor revolves, and when the rotor
revolves in this pulsating field it gives rise to a triple frequency emf. ;
that is, 30,000 per second in the illustration chosen. The con-
denser C5 has such a capacitance that the circuit i^CgCg resonates to
that frequency, and the 30,000-cycle currents in the rotor, in view
of the rate of rotation of the latter, cause a 40,000-cycle pulsation of
magnetic flux with respect to the stator windings. That in turn
induces a 40,000-cycle emf. in 8. Remembering that the antenna A
and the ground G constitute a condenser (see Section 137), which
I The following brief description of the Goldschmidt alternator is based on a fuller
one in Goldsmith's Radio Telephony, pp. 103-103, where further information may be
found. See also C. 74, p. 224.
164 RADIO COMMUNICATION.
has the same relation to the stator circuit that Cg has to the rotor
circuit, it is seen that by proper tuning the circuit SC^AG can be
made to resonate at the final frequency.
Thus by providing suitable circuits, it is possible to get a fre-
quency four times as great as that corresponding to the actual speed
and number of poles of the machine.
The principle has been explained as though the machines were
bipolar. Clearly, that would necessitate extraordinary speeds.
Instead, the large generators used in transatlantic service have
360 poles and are driven at 4000 r.p.m. by 250-h.p. motors. The
fundamental frequency is therefore 12,000, which is quadrupled
as has just been explained, giving 48,000 at the antenna. To secure
satisfactory operation the finest sort of workmanship is necessary
in building them.
E. Motors.
96. Uses of D.C. and A.C. Motors. — It has already been notedthat
an electric motor is almost identical with a generator in structure,
but its function is reversed; it converts electrical power into me-
chanical power. It is important to have the motor suited to the
kind of circuit on which it is to be used; a.c, or d.c, the right
voltage, etc. Common voltages are 110 to 120; 220 to 240; 500 to 550;
also, for a.c, 440. Lower voltages are used on battery circuits.
A.c. motors, like generators, may be single phase, two phase, three
phase, etc.; and d.c. motors may have series, shunt, or compound
excitation.
97. D.C. Shunt Motor. — If a shunt generator is used for charging
a storage batt*^ry and the engine is shut off, the generator will con-
tinue running, provided the battery is large enough, but an ammeter
in the circuit shows that the current has reversed. The battery is
discharging and the generator is running as a motor. The action
is explained by the fact that when a current is sent through a con-
ductor in a magnetic field, there is a force that tends to push the
conductor across the field (see Section 43). The left hand rule gives
the directions.
Consider the simple loop in Fig. 128, between the poles NS of an
electromagnet. If the wires + and — are connected to a source of
direct current, the iron will be magnetized. At the same time
current flowing in the direction of the arrows in the loop causes a
RADIO COMMUNICATION.
165
force toward the front in the conductor near the N pole and a force
toward the back in the conductor near the S pole. The loop turns.
The effect of the commutator is to make the rotation continuous,
by making the proper connection to the conductors as they come
into place.
By a line of reasoning very much like that for the d.c. generator,
we can pass from this simple case to that of a four-pole drum- wound
motor illustrated in Fig. 129. The directions of current and
rotation are shown by arrows.
Limiting Speed. — It might be expected that a shunt motor would
speed up indefinitely, but actually it soon comes to a definite speed,
Fia. ltd
Princijile oj
^hont Motor
and then continues to turn so fast, but no faster. As soon as the
armature begins to rotate, it generates an emf. according to the
right hand rule. This action is exactly the same as in a generator.
The emf. generated is opposite to the direction of current shown
by the arrows, and is for that reason called a "counter electromotive
force." The faster the- armature- turns, the greater the counter
emf. becomes. It cannot turn so fast that the counter emf. is as
great as the line voltage; because- then the two would balance,
there would be nothing to make the current flow through the arma-
ture, and consequently no pull to keep it turning. For example,
166
RADIO COMMUNICATION.
suppose the armature resistance of a certain motor is 0.25 ohm,
and suppose that a current of 4 amp. in the armature furnishes just
enough pull to keep it rotating. If the speed is high enough to
make the counter emf. 109 volts when the line voltage is 110, the
current is 4 amp.^
N
Fta. ns
Fia. 129.— Diagram of circuits of a 4-pole shunt motor.
Next, suppose the motor is driving machinery that calls for
five times as great a pull. The speed falls off a little. When it has
fallen enough to make the counter emf. 105 volts, the current is 20
E 1
»/=^ J5= 110-109= 1 volt. i:=0.25dhm. /=Q^ = 4amp.
RADIO COMMUNICATION. 167
amp.^ If that is enough to drive the load, the speed will be steady
at the new rate. So by changing its speed a very little, the motor
automatically takes more or less current, but always just enough
to drive its load.
The magnets are always of the same strength, regardless of load,
because the current around them depends only on the line volts
and the resistance of the field coils. It is entirely independent of
the current in the armature.
Comparison of Generator and Motor Actions. — In both generator
and motor we have an emf . developed in the armature by rotation
in a magnetic field. Also, in both we have currents which cause a
pull on the armature conductors. If the machine is to act as a
generator, its armature must be driven at such a speed that its emf.
is higher than the voltage at its terminals, due to emfs. in other
parts of the circuit. Then current flows with the emf. This cur-
rent causes a back-drag on the armature and makes it harder to
turn. If the machine acts as a motor, its emf. is lower than that of
the circuit to which it is connected. The current flows against this
motor emf., now called a counter emf., and causes a forward pull
on the armature which keeps it turning.
Starting Box. — ^The resistance of a motor armature is small. The
counter emf. developed by rotation is what keeps the current from
becoming excessive. When the motor is first connected to the
line, it is not rotating and there is no counter emf. Some other
way must be found to keep the current moderate. The simplest
way is to put resistance in series with the armature,^ and then
gradually reduce it ("cut it out") as the armature gains speed.
The resistance is usually in the form of wires or grids, mounted in a
ventilated iron box, the whole known as a "starting rheostat" or
"starting box.*' Various forms are used; Fig. 130 shows the con-
nections in one type. The parts drawn in solid lines are supported
on an insulating face plate, commonly slate. The internal connec-
tions are drawn in dashed lines. Fig. 131 shows how the starting
box is connected between the fused main switch and the motor.
When the resistance is all cut out, the iron strip K comes against
the electromagnet Jf, and the handle is held in place. If the switch
» J? =110-106 = 5 volts. /e = 0.25 ohm. / = Q-^ = 20amp.
* The field excitation is not cut down, but is of full strength from the start.
168
RADIO COMMUNICATION.
(Fig. 131) is opened, or the line becomes "dead" for any other
reason, the magnet ceases to hold K, and a spring S (Fig. 130) pulls
the handle back against the buffer J?, thus protecting the motor
against injury in case the current is turned on again.
A. A
4-
@ — -•
Starting boA for ohunt motor
L- CennecTlen To line P- Connection to ^hunt* -f leM
A-Conn«otion To 4krm«Ture .
T\
1 +
Fusea
3>witch
StArtin^
box
?\a. i3o
P 1 q. t3i
rnoTor
Connecti'orvs o^ ohun1" motor and sl^rtm^ box
Some starting boxes have four terminals. The internal connec-
tions of one box of that kind are shown in Fig. 132, and the con-
nections to the motor in Fig. 133. The extra terminal is marked
Zr— . It is needed because the electromagnet for the "no voltage
RADIO COMMUNICATION.
169
release " is connected directly across the line, the high resistance Z,
being contained in the box to keep the current for it small.
Connections to a starting box must be made according to the way
the terminals are marked on the box. They are almost always
— a
o -I
I
°0 — J
FiQ.i^e
starting box witl^ Two Mine' termindk
L+, L~, .line termindfs T- Connection to ohurit" field
A — Connection To apirvaTure
' +
Put5es
'\ < Switch 14, L-
TL__!ft
-6
box *
Fia.\35
AhunT
motor
Oonnectrond ^or o 3hor»T tnoTor «and sTArtin^
box v</ith Two line Terminals
stamped with letters or with the words * ' line, " " field, * * " armature, * '
but will not always be found at the places shown in Figs. 130
and 132.
170
RADIO COMMUNICATION.
At the motor the circuits are often brought out on a terminal
board after the fashion of Fig. 134. Care must be taken not to get
them confused, for example, by connecting the field in place of the
armature, or by making the sort of mistake shown in the right hand
diagram (marked ** wrong") of Fig. 134, where the "^'* terminal
of the starting box is wrongly connected to the junction of armature
and field, and the " — Line '* is wrongly connected to the armature
alone. Wrong connections are bound to cause trouble.
Starting and Stopping. — The proper operations for starting are:
1. See that handle of starting box is in the ''off" position.
2. Close switch (see Figs. 131, 133).
3. Move starting handle to first contact. Armature should begin
to turn. If it fails, open the switch at once, for something is wrong —
perhaps a faulty connection, loose contact, blown fuse, excessive
overload, wrong brush position, etc.
4. As armature gains speed, move handle over contacts, one step
at a time. Move slowly if load is great, taking if necessary as much
as 30 seconds. When the load is slight and the motor small, a few
seconds may suffice.
The operation for stopping is: Open main switch. In a few sec-
onds the handle should snap back sharply. If it fails, move it back
by hand and look for dirty contacts. Sometimes wiping the contact
studs and putting ou just a trace of vaseline will cure the trouble.
Very small motors, rated at a fraction of a horsepower, are often
connected directly to the line without a starting rheostat by simply
closing a switch.
Reversing Direction, — In the diagram (Fig. 134) the mains are
marked + and — . As a matter of fact, it makes no practical differ-
RADIO COMMUNICATION. 171
ence if the one marked + is really — , and vice versa. The motor runs
in the same direction. It can be reversed by taking off the two
connections at F (left hand diagram, Fig. 134) and interchanging
them. Care must be taken that the brushes rest on the commutator
at the right place and point the right way for smooth running, as
described in Section 106.
Speed Regulation and Control, — For reasons given under the head-
ing " Limiting speed " a shunt motor generally runs a little
more slowly when loaded (driving machinery) than when running
free. The change of speed is called the ''speed regulation.** For
most motors the regulation is good, the change in speed between no
load and full load being oi^y 5 per cent or less. Shunt motors are
therefore often called "constant speed" motors.
This supposes that the voltage applied to the motor is constant.
If it is too low, the speed falls off, as well as the power which the
motor can develop. If it is too high, the motor will overspeed some-
what and is likely to overheat and to spark injuriously at the com-
mutator. The speed can be changed, if necessary, by several
methods. Only two will be described.
A resistance in series with the armature circuit only (not the joint
line to armature and field) will reduce the speed. The conductor
must be large enough to carry the armature current without over-
heating. The ordinary starting rheostat will not serve, as it is not
made large enough for continuous duty. It would quickly overheat.
Sometimes special rheostats are provided for starting, which are
large enough to be left in circuit continuously. They are then
usually marked ''Regulating rheostat, for continuous duty."
The objection to this scheme is that it wastes power and that, if
the load changes, the speed changes too. It has the advantage of
being simple.
A resistance in series with the shunt field winding increases the
speed. This seems contradictory. The explanation is that when
the field current is reduced, the magnetism is weakened. The con-
ductors have to move faster to generate about the same counter emf .
as before, and since this counter emf. is always nearly as great as the
applied voltage the speed has to increase.
The objection to this method is that the motor may overspeed and
burst the armature by centrifugal force if too much resistance is used
in the field circuit. There is also danger of damaging the commuta-
tor by sparking. It is not wise to raise the speed more than 10 or
172 RADIO COMMUNICATION.
15 per cent above that marked on the name plate unless the
operator is very sure no harm will follow.
98. D.C. Series Motor. — ^The field coils of a motor may be made of
thick wire and connected in series with the armature, so that the
same current flows through both. It is then called a "series"
motor. The difference in connections, compared with a shunt
motor, is the same as for the corresponding kinds of generator. (See
Fig. 117.) Series motors differ in their behavior from shunt motors
in two important ways. They do not operate at constant speed, but
run very much more slowly when heavily loaded; and, at the lower
speeds they develop a large turning force. They are therefore used
on street cars, for cranking gasoline engines on automobiles, and
similar duty where high turning effort is wanted for starting a load.
Suppose there is some current, say, 5 amp., flowing in armature
and field coils. Now imagine the load to increase until the current
is 10 amp. Two things happen. If the magnetism remained the
same, the doubled armature current would cause double the pull.
But the magnetism does not remain constant. When the current
doubles, the field magnetism increases, because the 10 amp. flow in
the field coils as well as in the armature. Thus the doubling of the
armature current and the increased magnetization combined make
the pull much more than double. Also the stronger field would
make the counter emf . automatically increase if the speed remained
unchanged. But this is impossible because the counter emf. must
always be a little less than the line voltage, else no current will flow
to keep the motor going, so the speed must fall off.
The turning force mentioned above is called "torque". From
the explanation just given, the torque of a series motor at starting
is seen to be great, because at starting the speed is low and the
armature current large. The less the load, the higher the speed.
If the driving belt slips off, a series motor, unless^ it is quite small,
can overspeed enough to wreck itsdi;. Senear motors fsre^ih&eekuKf
direct connected or geared to the driven machinery. Shxmt
motors, on the contrary, will not over-speed and belts may safely
be used.
Speed Control. — The only way of controlling the speed of a series
motor that need be mentioned here is by using a rheostat. Except
for small motors, one is needed anyway for starting. If large enough
it can be left in circuit to keep down the speed. Of course this is
wasteful, because the heat produced in the rheostat uses electrical
power.
RADIO COMMUNICATION. 173
99. Ofher D.C. Motors. — Connected like compound generators
(Fig. 117), compound motors are used for special purposes, but
the worker with radio equipment is not likely to run across them
and for that reason they are not treated here. ^
100. Combination A. C. and D. C. Motors. — Reversing the current
in the line to which a series motor is connected has no effect on
the direction in which the armature turns. If the current is
reversed in the field coils alone, the magnetism is reversed, and
the armature turns the opposite way. Reversing the current in
the armature too, makes a second reversal of force, that is, the
armature turns as it did at the beginning. This is still true when
the reversals are so rapid that the current is truly alternating, so
the same motor can be used for a.c. and d.c. But in that case
some special construction is necessary; for example, the magnets
are built up of laminations, instead of being in a solid piece.
101. Induction Motors. — ^When the terminals of any coil are
connected to a circuit, the current sets up a magnetic field in and
around the coil. When a niunber of coils are arranged in the form
of a stationary two-phase or three-phase armature ^ and connected
to a corresponding two-phase or three-phase power circuit, there
comes the remarkable result, that the alternating currents, flowing
in the coils, produce, inside of the armature, a magnetic field which
rapidly and continuously revolves. The iron core and the copper
coils are both stationary; only the magnetism changes. If the
changes of current are made slowly, a compass needle placed in
the open space within the armature will spin just as if it were
directed by an imaginary magnet with its poles sliding along the
face of the armature.
Next, let an iron core with suitable coils on it be placed inside
this armature, on a shaft, so that it can turn. The revolving magnetic
field cuts across the conductors of this movable "rotor"; that sets
up emfs. ; currents flow, and now we have conductors with currents
in them in a magnetic field. Consequently the rotor begins to turn.
It speeds up until it turns nearly as fast as the moving magnetic
field. How fast that is depends on the construction of the station-
ary armature, and the frequency (cycles per second) of the alter-
nating current supplied.
I Compound motors are explained in Rowland, p. 126; Franklin and Estey, Dyna-
mos and Motors, p. 144; Timbie, p. 221.
« See Fig. 101.
174 SADIO COMMUNICATION.
The machine jnflt described is an ^'induction" motor. ^ Its
parts are called the stator (stationary part) and rotor (part that re-
volves) just as in an alternator. Nothing has been said about any
connection between the rotor and an external electric circuit. In
the simplest form of induction motor there is no such connection.
The rotor is dragged around magnetically at a practically constant
speed. A pulley on the rotor shaft can be used vdth a belt to
deliver power to some other machine.
In some forms of induction motor there are connections between
the rotor, which in that case has slip rings, and an external circuit.
But the external circuit is not a power circuit; it merely consists
of resistances for controlling the motor speed.
The terms *' squirrel cage" and ** wound" are often used to
describe rotors; the first means the simple kind with conductors
of plain bars of metal and no slip rings or other moving contacts;
the second means the kind having coils like an armature, and,
commonly, slip rings.
If one of the connections to a three-phase induction motor is
opened, leaving only two attached, the rotor continues to turn.
Two wires can supply only a simple a.c. (single phase), so it is
evident that an induction motor can be used on a single phase
circuit. But it will not start on a single phase without a special
starter.
Like d.c. motors, those for a.c. have to be operated at about
the voltage for which they were built. In addition, they have
to be connected to a line of the right frequency. Then they run
at certain definite speeds, which are nearly as high at full load
as when running free. On 60-cycle circuits, the conmion speeds
for small motors are a little under ISOO, 1200, and 900 r.p.m.
Starting. — Small induction motors are started by simply connecting
them to the right kind of power circuit by a switch, double-pole (two
blades, for two wires) for single phase, three-pole for three-phase, and
four-pole for two-phase motors. With polyphase (two or three-
phase) motors, this produces the revolving magnetic field as pre-
viously explained. With single phase, the action is different. It
was said, earlier in this section, that an induction motor will not
start on one phase, but will continue if started somehow. One way
1 For further explanation of action see Timbie and Higbie, A.C. Machinery,
Second Course, pp. 429-449; Franklin and Estey, Dynamos and Motors, pp. 340-362
Rowland, pp. 252-270.
RADIO COMMUNICATION. 175
might be to give it a start by hand. Generally that is not a practical
method. A second way is to use a ' 'phase splitter. " That merely
means that the current goes through the stator by two paths in
parallel, one having more inductance or capacitance than the other.
Inductance in any branch of a circuit causes a phase-lag in that
branch. The armature must have two sets of coils, and if the cur-
rents in them differ as to phase, the motor starts as a sort of two-
phase machine. After it gets up to speed, one winding (the * 'start-
ing" winding) is disconnected. That may be done by hand, a
special two-way switch being provided with a starting and a running
position or there may be an automatic centrifugal cut out in the
motor. ^
A third way is by ' 'repulsion motor" action. Then the rotor has
a commutator and brushes, like those for d.c. The stator is con-
nected to the supply line, the rotor is not. The brushes are con-
nected together by a short circuiting conductor. When currents
flow in the stator, other currrents are induced in the rotor' and it
begins to turn. At the proper speed, a centrifugal device short-
circuits the commutator and so converts the machine into a simple
induction motor. At the same time, the brushes are lifted automati-
cally, to reduce friction.
Larger three-phase motors are started by applying a fraction of full
voltage, obtained by a combined transformer and double-throw
switch known as a "compensator. " 3 "
F. Motor-Generators and Dynamotors.
102. Motor-Generators. — ^When electric current is to be had, but
not in the form needed, the change is made by transformers,* recti-
fiers, motor-generators or dynamotors, according to circumstances.
The first named, change a.c. at one voltage to another voltage at the
same frequency. The second, change a.c. to pulsating d.c. The
last two are used for changing a.c. at one frequency to a.c. at another
frequency or to steady d.c, or the reverse; also for changing d.c.
from one voltage to another.
1 Split phase starting is described in Timbie and Higbie, A.C. Electricity, Second
Course, pp . 510-512.
s See Timbie and Higbie, A.C. Electricity, Second Course, p. 514; Rowland, p. 270;
Franklin and Estey, pp. 383, 386; Standard Handbook, p. 542.
* For details, and other methods of starting, see Timbie and Higbie, A.C. Electric,
p. 454; Franklin and Estey, Dynamos and Motors, p. 360; Standard Handbook,
pp. 520, 1292, 1293.
« Described in Sec. 62.
176 RADIO COMMUNICATION.
The most easily understood way to make the change is by the use
of a suitable combination of motor and generator, built for the same
speed and mounted on a common base, the shafts being coupled
together. Such a combination is a ' 'motor-generator. "
Motors and generators have been described. The combination
brings no new ideas. Each part can be thought of by itself, without
regard to the other. Examples of such machines have been given.*
In radio practice they are used particularly for battery charging and
for supplying spark and arc circuits.
Battery Charging, — ^Motor-generators for battery charging are used
where the supply is a.c. or d.c. at the wrong voltage. In the latter
case if the d.c. voltage is too high, a rheostat may be used, but it
wastes power. When several low voltage batteries have to be
charged, they may be connected in series and the power wasted in
resistance thereby reduced.
The generator of a battery charging unit is usually shunt-wound.
The voltage of a storage battery rises as it gets charged. Also, at the
beginning it is allowable to use a larger current than toward the end
of the charge. The voltage of a shunt generator is lower when it is
delivering a large current than when the current is small.' There-
fore such a generator, connected to a discharged battery and given
the proper setting, produces a large current tv^hich gradually de-
creases as the battery yoltage rises. It is also possible to use a com-
pound generator, so designed that the voltage is substantially con-
stant, whatever the current, within the limits of the machine. In
that case the initial rate of charging the battery is higher than when
a shunt generator is used, but falls off in the same way. A high rate
of charging at the beginning cuts down the time required for the
whole process, and is therefore desirable, provided it does not injure
the battery. Modem portable batteries will stand charging in this
way and compound generators may consequently be used. The
proper treatment for a given battery must be learned from instruc-
tions pertaining to that particular form.
Motor-generators are used also for connection to ordinary lighting
circuits (about 110 volts) to get 500 or 600 volts d.c. for arc trans-
mitters, ^ or for connection to such circuits or to low voltage storage
batteries to get a.c. at 500 to 900 cycles for use with transformers in
audio frequency spark transmitters.* Such apparatus has been
described in Section 94.
1 Sec. 94, Figs. 121, 122, 124. » See Sec. 174.
2 Shown in Fig. 118. < See Sec. 154.
RADIO COMMUNICATION. 177
103. Rotary Converters, — If connections are made to a pair of
collector rings from opposite sides of a two-pole d.c. armature, it will
generate alternating current. At the same time, direct current can
be taken from the commutator. In that case the machine is a
"double current generator." If not driven by an engine, but con-
nected to a d.c. circuit, it operates as a shunt motor and can be used
to generate a.c. Operated on a.c. as a motor, it delivers d.c. When
used for such conversion, it is called a rotary converter. When an
a.c. generator is used as a motor (not an induction motor) it requires
d.c. for field excitation and operates at the exact speed (called'
* ' synchronous " speed), corresponding to the frequency of the supply.
The d.c. for the rotary converter field comes from the commutator.
On the other hand, when such a converter is used to generate a.c,
the frequency depends on the speed of rotation of the armature,
which can be controlled as previously described for the shunt motor.
The rotary converter has the advantage of accomplishing in a
single machine what the motor-generator does in two. Its dis-
advantage is that the voltage at the generator end depends entirely
on the voltage supplied to it as a motor, the a.c. voltage in the case
of a single phase converter being about 71 per cent of the d.c. voltage,
slightly more or less depending on the direction of the conversion.
Thus, if operated on a 10- volt storage battery, it would give about 7
volts a.c. Also, frequencies anything like 500 cycles, which it is
desirable to get in radio communication from d.c. with storage bat-
teries as a source, are impossible; either the speed or the number of
commutator segments would have to be increased beyond reason.
Instead of single phase, rotary converters can be built for two-
phase or three-phase currents, the former by four connections equally
spaced on the armature and four rings, the latter by three connections
and three collector rings. The statements made for bipolar machines
are equally true for multipolar rotary converters, if it is understood
that each ring has as many connections to the armature as there are
pairs of poles.
104. Dynamotors. — Rotary converters cannot be used for changing
direct current at one voltage to d.c. at another voltage. The most
compact machine for that purpose is the "dynamotor." An appli-
cation which will occur to the radio student is the securing of several
hundred volts for the plate potential of vacuum ti^ansmitting tubes
973400—19 12
178
RADIO COMMUNICATION.
from batteries giving only 10 or 12 volts. (See Fig. 135.) In the
dynamotor two separate armature windings are placed on a com-
mon core. One acts as a motor, the other as a generator. There is
but one frame and one set of field magnets. The two windings are
connected to commutators at opposite ends of the shaft. The ratio
of voltages is fixed when the machine is built, so the output voltage
pi«y
loV
Fig. 155
Double HI
3ooV.
Pyn*mo1br conn«eTion<s for conversion "from le to 3ee VcH"»
Ofc*
Arrndturf
Doubt« eurrsnt ^ener*Tor
for low Art«l hi^h voltA^e
n
Voir*^
S- iShunT coil^
D- PifferentUl eo'iU
Re^- > AA^IomAti'e r^Uo
J
depends on the voltage applied. The field coils receive current
from the same source as the motor armature.
105. Double Current Qenerators. — ^A dynamotor can be driven
by mechanical power as a generator, and can then deliver d.c. at
two different voltages. Slich machines have been designed for fan
drive on airplanes, the low and high voltages being used for the fila-
ment and plate currents, respectively, of vacuum tube transmitters.
To get constant voltages, in spite of the varying speed at which
RADIO COMMUNICATION. 179
the armature is driven, the field flux must be weakened as the speed
rises. Current taken from one commutator is sent around the field
coils, supplying the main magnetization. A weaker current from
the other commutator is sent around the opposite way, giving a
differential effect. (Fig. 136) . If the speed rises, and consequently
the voltage, the current in the second winding is made to increase
considerably by a sensitive automatic regulator. The flux is there-
fore reduced, counteracting the effect of the rise in speed.
106. Common Troubles. — ^Electrical machinery is subject to the
same troubles as other machinery, such as rough, gritty, dry or tight
bearings, bad alignment, sprung shaft, etc., which show themselves
by heating, taking excessive power, and vibration. The bearings
must be clean and smooth. Care must be taken never to spring or
jam the shaft. There must always be enough oil of good quality in
the oil wells to keep the bearings thoroughly lubricated. Most
generators and motors are oiled by means of brass rings that ride on
the shaft and dip into the oil and carry it up as they turn. Some-
times these are injured in taking the machine apart; then they do
not turn properly; the bearing runs dry and heats.
Some machines have ball bearings. They should run very easily,
but are subject to the same troubles as a bicycle bearing, such as
broken balls, grit, adjustment too tight. In general if a bearing
gets too hot to be borne with the hand, it needs attention; the
trouble is likely to grow worse, until finally the shaft binds firmly
and cannot be turned. The job of getting it free again may then be
a very tedious and troublesome one.
Another point of friction is at the brushes. If they are pressed in
too firmly, they rub harder than necessary. They should be fitted
smoothly so as to give the full area of electrical contact, then exces-
sive pressure will not be needed. They should be only tight enough
to make good contact and prevent sparking or flashing. When
carbon brushes are working properly, the metal surface on which
they rub becomes finely polished, and wears down very slowly.
This is particularly noticeable in the case of copper commutators
on direct current machines.
Besides those of a mechanical nature there may be electrical
troubles, some requiring expert attention, others easily found and
cured. The most common electrical troubles are caused by loose,
wrong or missing connections, and dirt.
180 RADIO COMMUNICATION.
Connections (usually accidental) that allow current to pass by a
piece of apparatus, instead of flowing through it, are called "short
circuits. '* They are a common source of trouble.
A systematic way of hunting troubles is as follows:
1. Make or find a circuit diagram, unless thoroughly familiar
with the connections and positive they are right. In drawing dia-
grams follow each branch of the circuit from the source (+ terminal
of battery or generator armature) completely around (through the
—terminal) to the place of beginning. Remember that no current
will flow in a circuit or in any part of a circuit unless there is a
difference of potential in it.
2. Trace the wiring according to the diagram.
3. While tracing, see that —
(a) Fuses are good, if any are in circuit.
(6) Connections are clean and good.
(c) Contact is not prevented by insulating caps of binding screws
or insulation of wire.
(d) Wires do not touch, making short circuits.
(e) There are no extra wires or connections.
(/) There are no breaks in wire inside of the insulation. This
occasionally happens with old lamp cord. The broken place is
very limber, and can be pulled in two more readily than a sound
place.
4. Look for defects in the apparatus itself.
In a generator, besides loose connections, electrical troubles easily
remedied are, for d.c. :
5. Failure to generate emf., caused by —
(a) Brushes not in the right place. On nearly all d.c. generators
of reasonably modern construction, the proper position for the
brushes on the commutator is nearly opposite the middle of the
field poles, or slightly forward (in the direction of rotation) of that
point. The exact location, found by trial, is that which gives
sparkless commutation. Brushes are set right at the factory, and
should be left as they are, unless there is good reason to believe that
they have since been shifted.
(6) Brushes not making good contact because of bad fit or too little
pressure. Test by lifting them slightly, one by one, to detect loose
springs; also try pressing brushes to commutator with dry stick.
Remedy by working fine sandpaper back and forth, sharp side out,
RADIO COMMUNICATION. 181
between commutator and brush (holding it in such a way that the
toe of the brush is not ground off) or by tightening brush springs, as
needed.
Brushes are designed, either to press against the commutator
squarely, pointing toward the center of the shaft, or, more commonly,
to trail somewhat as an ordinary paint brush might trail if held
against the commutator. However, there is also in very satisfactory
use a form of holder by which the brushes are held pointing against
the direction of rotation. Instead of sliding up or down in a box
they are pressed against a smooth face of brass by springs.
(c) Field connections reversed.
6. Sparking, when caused by
(a) Roughened commutator; cured by holding fine sandpaper
(not emery) against it while running.
(6) Brushes shifted; for remedy see 5, above. It is very impor-
tant that all brushes be at the proper points. This means, for
example, that if the brushes are supposed to touch at four points,
spaced a quarter way around the commutator, they shall, actually be
exactly a quarter of a circumference apart, as tested by fine marks
on a strip of paper held against the commutator.
7. Heating of commutator due to brush friction. Reduce tension
of springs.
In a.c. generators look for —
8. Loose connections and bad contacts at brushes. Position of
brushes on rings is immaterial, as there is no commutation.
In d.c. shunt motors, motor-generators, or dynamotors, the simple
troubles are:
9. Failure to start, or starting suddenly with speed quickly
becoming excessive, due to wrong connections. See Section 97.
10. Sparking, caused by excessive load or wrong brush position.
See 5 and 6 above. The proper position for motor brushes is
slightly backward, (against the direction of rotation) of the center
of the field poles.
CHAPTER 3.
RADIO CIRCUITS.
A. Simple Radio Circuits.
107. The Simplicity of Radio Theory.— The principles of alter-
nating currents developed in Chapter 1 are applicable to radio cir-
cuits. Radio currents are merely very high frequency alternating
currents. The fundamental ideas of sine waves (Section 50) apply to
what are known as continuous or "undamped waves.*' "Damped
waves " also behave in many ways like sine waves; for some purposes
slight modifications of the sine wave theory are needed. These are
treated in Part B below.
The frequencies of alternation of radio currents are very high.
Ordinary alternating current power circuits use frequencies from
25 to 60 cycles per second. The lowest radio frequencies, however,
lie above some 20,000 cycles per second, and the upper limit may
be put at perhaps 10,000,000 cycles per second. Such an enormous
difference in frequency should naturally give rise to some differences
in the behavior of radio circuits as distinguished from low frequency
alternating current circuits.
In low frequency a.c. circuits the principal opposition to the
current is offered by the resistance. The inductive reactance and
capacitive reactance are far greater than the resistance in a radio cir-
cuit, and resistance plays only a minor rdle. The reactance of such
small inductances as are provided by a few turns of wire is of im-
portance, and condensers whose small capacitance would very
effectually prevent the flow of ordinary alternating currents readily
allow the passage of radio currents. The mutual inductance effect
of one circuit on another is much greater, when radio frequencies
are used, than is the case with ordinary alternating current circuits.
The enormous frequencies used in radio work give rise also to much
larger skin effect, eddy currents, and dielectric losses than would
be the case if the same circuit were worked at low frequency.
Furthermore, measuring instruments commonly used for alter-
nating current work are, for the most part, imsuitable for use in
182
RADIO COMMUNICATION.
183
radio circuits, or require modified methods of connection. Instru-
ments whose indications depend upon the heating effect (Section 59)
are, in general, suitable for radio work. Direct current instruments
may also be used but in connection with rectifying devices. The
telephone receiver, so useful in low frequency work, requires a
rectifier also. At low frequencies, the diaphragm of the receiver
vibrates with the current, giving an audible singing note of the same
frequency as the alternating current. Radio currents execute their
changes, however, altogether too quickly to be followed by the
telephone directly, and even were it possible for the diaphragm to
vibrate so rapidly, the sound produced would be of too high pitch
to be heard by the ear. It is found to be necessary, therefore, to
break up the radio currents into groups of rectified waves. Each
1
Pia. 1^1
I
_c
Simple 5eri«s Circuit
L
b
group gives a single impulse to the diaphragm, and if the impulses
follow regularly with sufficient rapidity a musical note is produced.
108. The Simple Series Circuit. — ^The simplest form of radio cir-
cuit is one having resistance, inductance, and capacitance in series,
as in Fig. 137. An alternating emf . is supposed to be applied at E,
In Chapter 1, Section 57, it has been shown that the value of the
current produced in a circuit, to which an alternating emf. is ap-
plied, may be calculated by the equation,
Current=T
emf.
impedance.
If the effective value of the emf. is used here, the equation gives
the effective value of the current. (Sec. 51.)
The impedance Z depends not only on the resistance i?, but on
the reactance X of the circuit as well. (Sees. 55, 57.) For a sine
wave of applied emf.
Z^=R^+X^ (69)
184
RADIO COMMUNICATION.
That is, the square of the impedance is found by adding the
squares of the resistance and the reactance. The impedance can
therefore never be less than the resistance^ and may be very much
greater. If the resistance in the circuit is very small in comparison
with the reactance, the impedance is practically equal to the
reactance. The impedance is measured in ohms.
As has been pointed out (Sec. 49), the reactance is the opposition
offered to the current by an inductance or a capacitance. The
reactance of an inductance coil is equal to 2r times the frequency,
times the inductance. For a capacitance the reactance is equal to
2~fc ^^®^" ^^* ^° which / is the frequency and C is the capaci-
tance. In their reactive effects an inductance and a capacitance
tend to offset one another, so that the total reactance of an inductive
ceil and a condenser in series is found by taking the difference of
their individual reactances.
Example. — Let us calculate the reactance of the combination of a
coil of 500 microhenries inductance in series with a condenser of
0.005 mfd. capacitance at several different frequencies.
Frequency
cycles per
second.
Reactance of
ooU
(ohms).
Reactance of
condenser
(ohms).
Total react-
ance
(ohms).
60
1,000
100,000
100,700
1,000,000
0.188
3.142
314.2
316.23
3,142
-530,000
-31,840
-318.4
-316.23
-31.84
-530,000
-31,837
-4.2
-3,110
The table shows at a glance that the reactance of the coil is small
at low frequencies, increases as the frequency rises, and becomes
very considerable at the higher frequencies, such as occur in radio
work.
The behavior of the condenser is just the reverse. At the lowest
frequency it offers a very large reactance, but at radio frequencies
the impedance is vastly smaller. For very high frequencies the
reactance would be negligible.
In most radio circuits the resistance of the circuit can be kept as
small as a few ohms. It is therefore obvious that only in the case
of the 100,000 cycles, in the table, would it be necessary to take
account of the resistance in calculating the impedance.
RADIO COMMUNICATION. 185
For example, if -R=5 ohms, the impedance for the frequencies in
the table above, will have the values 530,000, 31,837, 6.5, 5 and
3110, respectively. In all except the third and fourth cases, the
difference between the reactance and the impedance is less than
one part in a million of the total.
It is thus apparent that in many cases the impedance of a circuit
depends almost entirely on the reactance of the circuit. Only in
those cases where the reactance is small is it necessary to take the
resistance into account.
109. Series Resonance. — It would seem at first sight, then, that
radio circuits would offer for the most part a high impedance and
that therefore very little current could flow, except with very
large emf . This is in general true of any radio circuit if the fre-
quency be taken at random. However, by properly adjusting the
value of the frequency, the reactance of the circuit may be made
zero. This is at once evident, when we remember that the inductive
reactance increases with the frequency, while the capacitive react-
ance diminishes. At some definite frequency, then, the inductive
reactance of the coil must have the same value as the capacitive
reactance of the condenser, and since they act against each other,
the total reactance will be zero.
This may be shown graphically. In Fig. 138 are plotted the
curves A and B of the reactances of the coil and condenser, respec-
tively, of the previous example. Frequencies are measured along
the horizontal axis and reactances along the vertical axis. The react-
ances of curve B are taken as negative to distinguish between the
opposing effects of the inductive and capacitive reactances. Curve
Cis obtained by taking the algebraic sum of the reactances of curves
A and B. It is the curve of resultant reactance in the circuit. For
the particular values of C and L chosen in this example, the circuit
acts like an inductive reactance at all frequencies greater than a
value of slightly above 100, 000 cycles, while below that point it has
the character of a capacitive reactance. Furthermore for only a
narrow range of frequencies, 99,000 to 103,000, perhaps, the reactance
of the circuit is less than 10 ohms. For most frequencies the react-
ance is much greater than this.
The frequency which makes the capacitive and inductive react-
ances equal is called the "resonance frequency" of the circuit, and
the circuit is said to be in ** resonance," or to be "tuned" to the
frequency in question. It is important to be able to calculate the
i
1
"la. iM
ntTren of
I.
K
Fiq. 140
1
/
'
1
«t
/
/•
«>,
^
-—
^
Fiq, ma
5.>>» c.-™,rt with
RADIO COMMUNICATIOX. 187
frequency for resonance. To do so, the condition must be fulfilled,
that
which shows that the frequency at resonance must be
Applying this relation to the example under discussion, and sub-
stituting therein L =0.0005 henry, C=5/10® farad, the resonance
frequency is foimd to about 100,700 cycles per second. The react-
ances of both the coil and the condenser at this frequency are the
same and have the value 316.2 ohms. This value may, of course,
be calculated by using for/ the value of the resonance frequency in
either of the expressions 2-KfL or 9—77^* It is of interest to note
that each of these expressions for reactance reduces simply to -*/^>
when the frequency has the resonance value.
There exists, then, for any series circuit containing inductance
and capacitance, a definite value of the frequency, for which the
total reactance in the circuit is zero, and the impedance is simply
. equal to the resistance of the circuit. This frequency is called the
resonance frequency, and the circuit is said to be in a condition of
resonance. The impedance has its smallest value, and the current
which flows in the circuit when the applied emf. has any value
whatever has the largest value possible with that value of fre-
quency.
These facts may be readily verified experimentally by inserting
in a simple radio circuit a suitable anuneter for measuring the cur-
rent. If now the frequency of the applied emf. is gradually raised,
the current will at first be small and will increase very slowly as the
frequency is increased. In the inmiediate neighborhood of the
resonance frequency, the current will suddenly begin to increase
rapidly, for small changes erf frequency, and after passing through
a maximiun, will rapidly decrease again as the frequency is raised
to still higher values. The results of such an experiment may be
shown by a curve in which frequencies are measured in the hori-
zontal direction, while the values of the current corresponding are
188 RADIO COMMUNICATION.
plotted vertically. Since most instruments suitable for measuring
radio currents give deflections proportional to the square of the cur-
rent, it is customary to plot the squares of the current, or the deflec-
tions of the instrument, rather than the current itself. Such "reso-
nance curves " are plotted in Fig. 139, and they show plainly the
"resonance peak."
On account of its great importance in radio work the phenomenon
of resonance requires further study. To fix our ideas, let us suppose
that a circuit whose inductance and capacitance have the values
already chosen in the previous example, has a resistance of 5 ohms
and that an emf . of 10 volts is applied in the circuit. The maximum
possible value of the current is found by dividing the applied voltage
by the resistance, which gives 2 amp. This current will flow when
the frequency has the critical value of 100,700 cycles per second.
To study the distribution of emf. over the different parts of the cir-
cuit we have to remember (Sec. 55) that the emf. between any two
points of the circuit has to have a value equal to the product of the
current by the impedance between the two points. Accordingly
the emf. between the ends of the resistance is 2X5=10 volts, that on
the coil is 2X316.23=632.46 volts, and the same emf. is found
between the terminals of the condenser also.
The existence of such a large voltage on both the coil and the con-
denser explains how it is possible to obtain such a relatively large
current through the large reactances of the'coil and condenser. The *
small applied voltage is employed only in keeping the current flow-
ing against the resistance of the circuit, not for driving the current
tiu'ough the coil or condenser. To explain the presence of the large
voltages on coil and condenser, it must be remembered, as was shown
in Section 59, that when a current is flowing through an inductance
and capacitance in series, the emf. on the inductance opposes that on
the capacitance at every moment. The sum of the voltages on the
two is therefore found by subtracting their individual values.
Since at the resonance frequency the emf. on the inductance has the
same value as the emf. on the capacitance, the emf. between the
terminals of the two in series is therefore zero.
Energy is supplied to the circuit by the source at a rate which may
be determined (when the resonance condition has been established)
by simply multiplying the emf. by the current. (Sec. 55.) That is,
in the present instance, the power is 10X2=20 watts. The power
dissipated in heat in the resistance may be calculated by taking the
RADIO COMMUNICATION. 189
product of the resistance by the square of the current. (Sec. 51.)
In this case it is 5X2^=20 watts. The source, therefore, supplies
energy to the circuit at just the right rate to make good the energy
dissipated in heat in the resistance. After the current has reached
the final effective value (2 amp. in this case), no further energy is
supplied to the coil or condenser by the source, but their energy is
simply transferred back and forth, from one to the other, without loss
or gain in the total amount, nor is any outside agency necessary to
maintain this condition.
Mechanical Example of Resonance. — ^Many mechanical examples of
resonance might be cited. It is a well known fact that the order to
** break step" is often given to a company of soldiers about to pass
over a bridge. Neglect of this precaution has sometimes resulted in
such violent vibrations of the bridge as to endanger it. This is espe-
cially the case with certain short suspension bridges.
When a shock is given to a bridge it vibrates, and the frequency of
the vibrations, that is, the number of vibrations per second, is
always the same for the same bridge, whatever the source of the
shock. The frequency of vibration is analogous to the resonance
frequency of the circuit. For if an impulse be applied to the bridge
at regular intervals, tuned so that the number of impulses per second
is exactly equal to the number of vibrations natural to the bridge in
the same time, violent vibrations may be set up, although the indi-
vidual impulses may be small. In fact, when the bridge is thus
vibrating, the impulses need to have only just force enough to over-
come the frictional forces and thus keep the vibrations from dying
away. The much greater forces involved in the vibrations them-
selves corresxwnd to the large voltages acting on the coil and conden-
ser. The voltage on the condenser is of the same nature as the large
forces which exist in the beams of the bridge when they are stretched,
while the voltage on the coil corresponds to the very considerable
momentum of the moving bridge. The small force of the impulses
given the bridge corresponds to the small applied emf . in the elec-
trical case.
If the vibrations of the bridge ever become so violent as to rupture
it, it means that the beams have been stretched beyond their break-
ing point. Similarly, the dielectric of the condenser may be
broken by the emf. existing between its terminals, in cases where
the resonance current is too larnre.
190 RADIO COMMUNICATION.
110. Tuning the Circuit to Resonance.— ^The practical importance
of resonance lies in the fact that it enables the impedance of a
circuit to be made equal to the resistance alone. It must be
remembered that the reactance of the small inductances in the
circuit, which are unavoidable, become important at radio fre-
quencies and may often be much greater than the resistance.
This fact, taken in connection with the smallness of the emf.
of incoming signals, would make it impossible to obtain any but
minute currents in the receiving apparatus with inductance alone
in the circuit. From this standpoint, the sole function of the
tuning of the circuit to resonance is to offset the* inductive react-
ance by an equal capacitive reactance, so that the impedance may
be made as small as the resistance.
The circuit may be tuned to resonance in three ways —
(a) By adjusting the frequency of the applied emf.
(b) By varying the capacitance in the circuit.
(c) By varying the inductance in the circuit.
Of these, the first case has already been treated. The other
two find application in receiving circuits where the frequency
of the incoming waves is beyond the control of the operator in the
use of coupled circuits and in the adjustment of the frequency of
the waves emitted in certain methods of sending.
The possibility of tuning a circuit is of course not confined to
radio circuits, but is present also with ordinary alternating current
circuits, and is becoming common in telephone work. However,
at low frequencies the values of the inductance and capacitance
involved are relatively great, so as to make it inconvenient to vary
their values in steps sufficiently small. Furthermore, in low
frequency work the reactances of the coils likely to occur in the
circuit are small, and the large quantities of power involved render
the use of condensers relatively uncommon. The inductances
and capacitances used in radio work, on the other hand, are rela-
tively small, and the construction of coils of continuously variable
inductance (variometers or variable inductors) and of apparatus
of variable capacitance (variable condensers) offers no particular
difficulties.
From formula (71) it appears that i^ is the product of the induc-
tance and capacitance, rather than their actual values, which de-
tennine the resonance frequency. To tune a circuit to a given
frequency, the inductance may be large or small, provided only
RADIO COMMUNICATION. 191
that the capacitance may be bo adjusted that the product of induc-
tance and capacitance shall have the value corresponding to the
frequency assumed.
111. Resonance Carves. — ^A resonance curve is a curve which
shows the changes of current in a circuit, when changes are made
which cause the resonance condition to be somewhat departed from.
For example, the current (or square of the current) may be plotted
for different values of the frequency somewhat above or below the
resonance frequency. Or, the curve may show the change in
current, when the capacitance (or inductance) is somewhat raised
and lowered with respect to the value which holds for the condition
of resonance. Such curves are often determined experimentally,
in whole or in part, on account of their value in calculating the
damping of the circuit. (Damping is treated in Sec. 116 below.)
Such, for example, are the curves of Fig. 139, in which are plot-
ted the values of the current squared, to some arbitrary scale, for
different values of the capacitance of the variable condenser. The
inductance of the circuit was fixed at the value 377 microhenries
Three different curves were determined with the resistance in the
circuit fixed at the values 4.4, 9.4 and 14.4 ohms, respectively.
Sharpness of Resonance. — It was of course to be expected that
the value of the current at resonance (height of the peak), should be
greater, the smaller the resistance in the circuit, but attention needs
to be called particularly to the sharpness of the curve with the
smallest resistance and to the flatness of the curve with greatest re-
sistance. This is the characteristic of resonance curves in general,
and is a necessary consequence of the equations for the impedance.
It may be shown still more clearly, if the scales to which the three
curves are plotted are so altered that the peaks of the three curves
have the same height. This has been done in Fig. 140.
The same results may be seen by calculating the square of the im-
pedance with different settings of the condenser and with different
resistances in the circuit. The resonance frequency in this case was
169,100 cycles per second, which shows that with the inductance
of 377 microhenries the setting of the condenser at resonance is almost
exactly 2350 mfd. The reactance of condenser and coil at this fre-
quency is 400.56 ohms in each case.
The following table shows the impedances for three different set-
tings of the condenser when the resistance of the circuit has the three
values corresponding to those of the curves. The squares of the cur-
192
RADIO COMMUNICATION.
rents are, of course, less in proportion as the squares of the impedance
are greater.
Setting of
condenser
(micro-mfd).
Impedance squared.
For J^ -4.4
For R=9A
For i2=14.4
2309
2350
2400
94.1
19.3
90.0
163.1
88.3
158.9
282
207
278
For the smallest resistance, the square of the current is about 4.7
times as great at resonance as when the capacitance is changed by
50 micro-mfds. in either direction. For 9.4 ohms in circuit the ratio
is about 1.8, and for the largest resistance, only about 1.35. These
calculated ratios agree very well with the experimental values.
The close connection of the shape of the resonance curve with its
resistance, points to the possibility of calculating the total resistance
in the circuit from measurements of the resonance curve. For this
method of measuring radio resistance see 0. 74, Sections 49 and 50.
The calculations here given, as well as an inspection of the curves of
Fig. 139, show that the resonance curve is not symmetrical. That
is, the current has not the same value when the capacitance is a cer-
tain amount less than the resonance value, that it has when the value
of the capacitance is greater by the same amount. The question of
this lack of symmetry is treated in the next section.
Symmetry of Resonanre Curves. — The curves of Fig. 138 show the
changes of coil reactance, curve -4, and condenser reactance, curve
By together with the total reactance, curve C (their sum) when the
frequency is changed. The curve of total reactance is not symmetri-
cal about the axis where it passes through its zero value (point Z,
Fig. 138). The resonance peak (Fig. 139) is, therefore, unsymmetrical
also. That is, the current is not the same for two frequencies, one
slightly higher than the resonance frequency, and the other the same
number of cycles lower than the resonance frequency. The expla-
nation is found in the shape of the curve of condenser reactance.
The same lack of symmetry exists when the inductance and the fre-
quency are held constant and the capacitance is varied to obtained
resonance, because the shape of the curve of condenser reactance in
this case is the same as in the preceding. However, if the frequency
and capacitance are held constant, and the resonance condition is
reached by varying the inductance, a symmetrical resonance peak is
RADIO COMMUNICATION.
193
obtained; equal changes of the inductance, above and below the
setting for resonance, will cause the current to fall to the same value.
The difference of this case from the two preceding lies in the fact that
curves of condenser and coU reactance and hence of total reactance,
are here straight lines.
To summarize then, the resonance curve is symmetrical when the
tuning is accomplished by varying the inductance (C and /constant),
but is not symmetrical in the two other methods of tuning, viz., by
varying the capacitance (L and / constant) or by varying the fre-
quency (Cand L constant).
112. The Wavemeter. — The phenomenon of resonance enables
one to obtain relatively large currents in a circuit to which only
r
it
A
o
if.
JVL
Fia.Mt
Fia. Ml
5im ^le Wdvem«Ter circw'iT
I Ml I •••II
lndi*CAter
Circuit
Waviameler with cou^f«cf |ndi'e*Ter
'It
le
if
R»ri«llel cireuii'
having cA^eitknc*
in )>4ittlle( witK
\ndocXAnem i r»i»1fcnoi
a small emf. is applied, provided only that the circuit is properly
tuned. To determine when the condition for resonance is realized
with a given frequency in a given circuit, or to measure the frequency
at which a circuit of predetermined constants should be in resonance,
use is made of the "wavemeter.*' This is the most important
instrument used in radio measurements. It consists essentially
of a series circuit, which includes an inductance and a capacitance,
both of which are of known values. Either the inductance or the
capacitance may be of fixed value while the other will be variable.
A hot wire ammeter, thermo-j unction, or other suitable device for
measuring radio currents is inserted, either directly into the circuit
(Fig. 141), or, better, is coupled electromagnetically to it, the cou-
97340*'— 19 13
194 RADIO COMMUNICATION.
pling being made as loose (Sec. 119) as will pennit of a suitable max-
imum deflection of the ammeter (Fig. 142).
If the frequency of the current in a given circuit is to be measured,
the coil of the wavemeter circuit is placed near the circuit in ques-
tion, and the capacitance of the wavemeter is varied, until the
indicating device shows that the current in the wavemeter circuit
is a maximum. In making the final adjustment the wavemeter
coil should be moved as far away from the circuit in question as
is possible and yet provide a convenient maximum deflection of the
ciurent indicating device.
From the known value L of inductance of the wavemeter coil
and the capacitance CV, corresponding to the setting of the con-
denser at resonance, the desired frequency may be calculated
from equation (72) which gives
What is generally desired, however, is not so much the frequency
as the wave length (Sec. 124) of the electromagnetic waves radiated
by the circuit. The wave length X is connected with the frequency
/ by the fundamental relation
X=j (73)
in which c is the velocity of electromagnetic waves in space and
has the value of 300,000,000 meters per second. Expressing Cf
in mfd. and L in microhenries, as is commonly conveirient, the
fundamental wavemeter equation giving the wave length in meters
is
\=^\%U^lLC, (74)
For example, if Z=1000 microhenries and Cp=0.001mfd., the wave
length emitted by the circuit is 1884 meters.
A wavemeter is usually provided with a buzzer or some other
auxiliary device by means of which oscillations may be set up in
the wavemeter circuit. These will have a wave length which
may be calculated by equation (74) from the inductance and capaci-
tance of the wavemeter circuit. By coupling any desired circuit
with the wavemeter circuit an emf . is introduced into the former,
when the buzzer is working, the frequency of which is the same as
that existing in the wavemeter circuit. This frequency may be
calculated by (74) from the known inductance of the wavemeter
RADIO COMMUNICATION. 195
coil and the capacitance corresponding to the setting of the conden-
ser. If, further, it is desired to tune the circuit in question to the
frequency emitted by the wavemeter circuit, it is only necessary
to couple the current indicator to the circuit to be tuned, to cause
the wavemeter to emit waves and to vary the capacitance or induct-
ance of the circuit to be adjusted, until the indicator shows a maxi-
mum current.
113. Parallel Resonance. — In the preceding sections it has been
shown how to obtain the maximum current in a circuit for a given
applied emf. The principle of resonance, utilized for this purpose,
finds application also in the solution of the reverse problem of
keeping currents of a certain frequency out of any chosen part of a
circuit without, however, preventing the passage of currents of
other frequencies. To such an arrangement is given the appropriate
name of a ''filter." A filter consists essentially of an inductance
coil, joined in parallel with a condenser. This combination is
interposed between the emf. in question and that portion of the
circuit from which the undesirable currents are to be excluded.
Any such combination of inductance and capacitance, taken at
random, will oppose currents of a single frequency only, whose
value depends principally on the values of the inductance and
capacitance. To render such an arrangement effective against
currents of a certain chosen frequency, it is necessary to adjust the
capacitance and inductance to have a definite relation. The solu-
tion of this problem requires a- knowledge of the principles of ''paral-
lel resonance."
Fig. 143 shows a coil of inductance L and resistance R. joined
in parallel with a- condenser of capacitance C The current / flows
from the alternating source of emf. E, through the main circuit,
and at the branch point divides, a part Ii flowing through the coil,
and the remainder, Ic through the condenser. At every moment,
the current / has a value which is the algebraic sum of the values
of // and Ic existing at that same moment. Let us suppose, first,
that the emf. E has a definite frequency, and that the inductance
of the coil is invariable. Current measuring instruments may be
arranged to measure the three currents. If the capacitance is varied
continuously, and the indications of the ammeters recorded, the
following experimental facts will be observed.
In general, the currents in the coil and condenser will be unequal,
and the current / may be less than either. As the capacitance is
varied, the currents in the coil and condenser may be made to
19i
BADIO COMMUNICATION.
approach equality, and at the same time the main cuirent will
decrease. At lei^th, for Bome critical value of the capa<Jtance, the
main cutrent will reach a very Btuall miniinti"! value, while the
curreat in the coil and the condenser current are nearly equal.
Further, each is many times laiger than the main current. As the
capacitance is now varied etill further, the main current begins to
increaae, and the coil and condenser currenta are no longer bo nearly
equal.
Ah aa example, awume the inductance of a coil to be lOOO
microhenries and its resistance 2 ohms. An effective emf. of 10
volte and a frequency of 71,340 cycles per second is applied. (This
1
f)Q.IAS
l|.=...
value of frequency was chosen, s
It gives
current I,
with a condenser of almost exactly 0.005 mfd.) The changes of the
current in the main circuit, as the capacitance is varied from 0.002
to 0.008 mfd. are shown in Fig. 144, in which values of the capaci-
tance are measured horizontally and values of the square of the
current vertically. The latter values in the figure are multiplied
by a million. The minimum current is not zero, but its value is
only about 0.0001 amp., a value whose square is too small to be
easily distinguished in the figure. The correepondii^ currents in
the coil and condenser are each about 0.02236 amp. Their difference
RADIO COMMUNICATION. 197
is only about 1/100,000 part of this value, the condenser current
being the larger by this minute amount.
In practice, then, if we imagine some troublesome emf. to be
introduced into the circuit at E (Fig. 143), by induction or otherwise,
the employment of a parallel combination of inductance and capac-
itance can be made to very completely prevent this emf. from
causing currents to flow in the circuit, provided only that the values
of inductance and capacitance are properly chosen. And such a
filter does not prevent the passage of currents of other frequencies.
If, for example, we suppose that the emf. E has a frequency of
100,000 cycles, in the above case the combination of 1000 micro-
henries and 0.005 mfd. would allow 0.01549 amp. to flow in the main
circuit. That is, this filter has 155 times as much stopping ei^ect for
currents of 71,340 cycles per second as for currents of 100,000 cycles,
and for frequencies further away the effect would be greater. Fil-
ters of this kind are used in airplane radio telephone sets to remove
noises produced by the electric generator used in the set; for example,
in the type SCR-68 sets. A similar filter is used in connection with
the type EEJ-1 buzzerphone.*
The results of theory show that to filter out ciurents of a frequency
/, the necessary relation between inductance and capacitance is
given in the following equation:
The current in the main circuit is, under this condition,
In all practical radio circuits, however, the resistance of a circuit is
so small in comparison with the inductive reactance, that it may be
neglected. The equation (75), undqr these circumstances, goes over
into the same equation that holds for series resonance, that is —
Otherwise expressed, then, it may be stated, that when the con-
dition of parallel resonance is realized, the loop circuit which con-
tains the coil and condenser in series is very closely in a condition
1 See S. C. Electrical Engineering Pamphlet No. 1.
198 RADIO coMMU^'ICATIo^^
of series resonance. Recalling the fact that, in the series resonance
condition, the emf. on the condenser is equal and opposite to that
on the coil, it is easy to see that there is here a flow of current back
and forth between the coil and condenser. Viewed from the main
circuit (Fig. 143), the current in the coil is,at every moment, oppo-
site to the condenser current, so that the main current, which is their
algebraic sum, is at every moment merely the difference between
the condenser and coil currents. These latter being nearly equal
in value, we have the explanation of the existence of the relatively
large currents in the coil and condenser, when the main circuit is
almost free from current.
The ideal filter would be one in which the resistances of the in-
ductance coil and all the connecting wires in the two branch circuits
were actually zero. In such a case, the condition for parallel reso-
nance would be rigorously the same as for series resonance, equation
(70), the condenser current would be exactly equal to the current-
in the coil, and absolutely no current would flow in the main circuit.
The filter effect would be perfect. No energy would therefore flow
from the source E, but this would merely give the condenser an
initial charge, and thereafter current would flow between the two
branch circuits, even if the main circuit were removed . See Section
115, on free oscillations.
In any actual case there must, however, be some resistance in the
circuit, and the energy for the heating in the resistance must come
from outside. The emf. E must cause just enough current to flow
in the main circuit to make good this loss of energy. It is easy to
show that these conclusions follow also from the equations previ-
ously cited. When the resonance condition is established, the main
current and the emf. E are in phase, so that the power is equal to
E^R
the product of the emf. E and the main current, that is, to d2T79~T7^*
The power lost in heating is equal to the square of the current in
the coil multiplied by the resistance of the coil. The current in the
E
coil is, however (Section 57), -7— ^7^7^====, so that the power in heat-
E^R
ing has the value 7>2_[_/2 fj, 2 ^^ before. The fact that the main
current should be zero, when the resistance is zero, is in line with
equation (76) for 7, and with the fact also that the heating must be
zero in that case.
RADIO COMMUNICATION. 199
Besides tuning the filter by varying the capacitance, it is of course
possible to obtain parallel resonance by varying the inductance
instead. For a given coil and condenser, it is also possible to obtain
parallel resonance by adjusting the frequency of the applied emf.
It must be noted, however, that when either the inductance or the
frequency is varied, the conditions for minimum current in the main
circuit are slightly different and are not the same as when the
capacitance is varied. These three conditions differ appreciably
only when the resistance is large. For radio circuits, the resistance
is usually so small that no difference can experimentally be detected
between all these conditions for minimum current. For zero
resistance, all three coincide and are expressed by equation (75).
114. Capacitance of Inductance Coils. — ^A coil used in radio cir-
cuits can seldom be regarded as a pure inductance. While the
capacitances between turns of a coil are small, they approach the
same magnitude as other capacitances used in radio circuits. A coil
is to be considered as a combination of inductance and capacitance
in parallel. It is found that the capacitance Co of a coil does not
change appreciably with frequency. Neither does the inductance
itself, but the apparent or equivalent inductance La of this com-
bination of inductance and capacitance does vary with frequency
as indicated by the equation
The variation with wave length is shown in Fig. 145. When the
coil is the main coil of a circuit, it is usually desirable to introduce
the emf. into the circuit by induction in the coil itself rather than
in series with the coil. The capacitance of the coil is then merely
added to the capacitance of the condenser. T\Tien the emf. is in
series with the coil, one effect of the coil capacitance is to increaee
the resistance introduced into the circuit by the coil and thus
reduce the current.
The capacitance of coils frequently give rise to peculiar and
undesirable effects in radio circuits. Among these are effects
caused by the capacitances of those parts of a coil which are not
connected in the circuit. The turns which are supposedly **dead''
may actually produce considerable effect, both upon the resistance
and frequency of resonance of the circuit. Thus, the capacitance
200
RADIO COMMUNICATION.
of the iinused part 2 of the coil in Fig. 146 causes a second circuit
to be closely coupled to circuit 1. This may cause the circuit 1 to
respond to two frequencies and exhibit the other phenomena of
coupled circuits described in Section 120 below. (See also 0. 74,
Sec. 19.)
B. Damping.
115. Free Oscillations. — Thus far it has been assumed that a con-
stant alternating voltage has been applied to radio circuits, in which
case the alternating currents produced are of constant amplitude.
Such currents may be regarded as analogous to the forced oscillations
which are produced in a mechanical system like a swing or a pendu-
lum, when it is acted upon by a force which varies periodically.
c. ^'"^
'•^'^^,.
F I a. 141
1
~t S 5
1 • 1
L
c ^
\
CTCCXTfCX
^ !
-i|i|iHi .H
i& s
K
^U^XlX^J^XXx^f^xxxxxj J
E
ff«ct of eTietri buteJ cA^Acify
n tt>« unuA««f Turns of A coil
The system is forced to vibrate with the same frequency as that
of the force.
It is, however, possible to produce oscillations of current in a
circuit without the necessity of providing a source of alternating emf .
A common method is merely to charge a condenser and then to
allow it to discharge through a simple radio circuit.
This may be accomplished, for example, by the simple means
shown in Fig. 147. By throwing the switch S to the left, the
condenser C is charged by the battery E, but when the switch is
thrown to the right, it is discharged into the circuit containing the
resistance JR and the inductance L. If the resistance JR is not too
great, electric oscillations are set up which, however, steadily die
away as their energy is dissipated in heat in the resistance. As in
Fig. 148, the current becomes less and less as the oscillations go on.
To explain this action, we must follow more closely what takes place
in the circuit from the moment when the condenser, charged up to a
RADIO COMMUNICATION.
201
certain potential difference, is inserted in tlie diecbai^e circuit.
WhenthecondenserBtarts todiBcha^eitaelf, a current flowa out of it,
and the potential difference oC the plates decreases as a rmilt. At
the moment when the plates have reacl^ the same potential, ciurent
is still flowing out of the condenser. The current has energy and
cannot be stepped ingtantly. In fact, to bring the current to zero
value, it is necessary to oppose it by an emf., and Ibe amount of emf.
ri<a.M4
necessary is greater the more quickly one wishes to atop the current.
It is similar to the case of a movii^ body. On account of its motion
the body possesses enei^, and cannot be brought to rest instantly.
The greater the force which is opposed to it, the more quickly it may
be brought to rest; but unless its motion is opposed by some force, it
continues to move indefinitely without change of velocity.
202 RADIO COMMUNICATION.
The flow of current from the condenser, then, does not cease when
the condenser has discharged itself, and, as a result, that plate which
was originally at the lower potential takes on a higher potential than
the other. The condenser is beginning to charge up in the opposite
direction. The potential difference of the plates now acts in such a
direction as to opposfe the flow of the current, which decreases con-
tinually as the potential difference of the plates rises. If the resist-
ance of the circuit were zero, the current would be zero (reversing)
at that moment when the potential difference of the plates had become
just equal to the original value. That is, the condenser would be as
fully charged as at the beginning, only with the potential difference
of the plates in the direction opposite to that at the start. Now begins
a discharge of electricity from the condenser in the opposite direction
to the first discharge, and this discharging current flows until the
condenser has become fully recharged in the original direction. The
cycle of operations then repeats itself, and so on, over and over
again.
The action in the circuit may thus be described as a flow of elec-
tricity around the circuit, first in one direction and then in the other.
The rate of flow (current) is greatest when the plates have no poten-
tial difference, and the current becomes zero and then begins to build
up in the opposite direction at the moment when the potential differ-
ence of the plates reaches its maximum value. This alternate flow
of electricity around the circuit first in one direction and then in the
other is known as an *' electrical oscillation." Since no outside
soiu*ce of emf., such as an a.c. generator, is acting in the circuit, the
oscillations are said to be "free" oscillations.
Mechanical free oscillations are well known. Such, for example,
are the swinging of a pendulmn, and the vibration of a spring which
has been bent to one side and then let go. In the case of the pendu-
lum, the velocity with which it moves corresponds to the value of the
current in the electrical case, while the height of the pendulum bob
corresponds to the potential difference of the condenser plates.
When the bob is at its highest point, its velocity is zero, corresponding
to the condenser when the plates are at their maximum potential
difference and no current is flowing. When the pendulum bob is at
its lowest position, it is moving most rapidly. Similarly, when the
plates of the condenser have zero potential difference, the current
flowing has its maximum value. The pendulum does not stop mov-
ing when it passes through its lowest point; neither does the current
cease at the moment when the condenser plates are at the same po-
raOio communication. 203
tential. The pendulum rises with a gradually decreasing velocity
toward a point at the other end of the swing as high as the starting
point. The current gradually decreases as the condenser chaises up
to an opposite potential difference equal to the original value. The
return swing of the pendulum corresponds to the flow of current in
the direction opposite to the original discharge.
A pendulum swinging in a vacuum and free from all friction
would continue to swing indefinitely, each swing carrying it to the
same height as the starting point. Similarly, electric oscillations
would persist indefinitely in a circuit, that is, they would be "un-
damped " if there were no resistance to the current.
Actually, electric oscillations die down in a circuit and finally
cease altogether, just as an actual pendulum will make shorter and
shorter swings and finally come to rest. Since the occiurence of
free oscillations in a circuit presupposes no interference with the
circuit from outside, the circuit receives no energy beyond that
imparted to it at the moment when the oscillations begin. There-
after the circuit is self-contained, and any loss of its energy in heat
and electromagnetic waves reduces by just so much the energy
available for maintaining the oscillations. This loss of energy goes
on continuously and the oscillations die away to nothing. They
are said to be ''damped" oscillations.
At the start there is a definite amount of energy present in the
circuit, namely, the energy of the charge given the condenser.
The amount of this energy depends upon the capacitance of the
condenser and the square of the potential difference between its
plates (emf. to which it is charged). This energy exists in the
dielectric of the condenser, which is in a strained condition due to
the charge. As soon as the current begins to flow the condenser
gives up some of its energy, and this begins to be associated with
the current and is to be found in the magnetic field around the cur-
rent, that is, principally in the region around the inductance coil.
As the current rises in value imder the action of the emf. of the con-
denser, energy is continually leaving the condenser and being stored
in the magnetic field of the inductance coil. When the plates of
.the condenser have no potential difference, the whole energy of the
circuits resides in the magnetic field of the coil and none in the
condenser. Energy is then drawn from the coil as the current de-
creases and energy is stored up in the condenser as it is recharged.
If the resistance of the circuit were zero and no energy were
radiated in waves or dissipated in other ways, the total energy of
204
RADIO COMMUNICATION.
the circuit would be constant. The energy dissipated in heat and
electric waves is, however, lost to the circuit, so that the total amount
of energy, found by adding that present in the condenser to that in
the inductance, steadily decreases. Finally all the original store of
energy given the circuit has been dissipated and the oscillations
cease.
The energy lost when a steady current is flowing in a circuit de-
pends not only on the value of the current, but on the resistance
of the circuit, and in a radio circuit this resistance is replaced by a
somewhat larger quantity of the same kind, the ^'effective resist-
ance." (See Sec. 117.) The greater the effective resistance, the
greater the amount of energy dissipated per second when a given
current flows.
Ohm's law shows that to keep a current I flowing through a resist-
ance R an emf. i^Jis necessary and this has to be furnished by the
Fl<3. K9
VibrAtion of «
s^rir^ clamed
FjO ISO
r. . -g ,--_•.---« 1«; . •. \
■■•■Ml:::..:j.^J.Ja-:..:
Lmf induced in the .croAs ftcefion of «
Conductor CArr^ir^ hi^ frequency current
battery, generator, or other source. In an oscillating circuit the
same is true, and that portion of the emf. in the circuit which is
employed in forcing the current against the resistance is of course
not available for charging the condenser or building up the dis-
charge current. The changes of current in the circuit described above
are thereby hindered, and the current does not rise to as great a value
as it would in the absence of resistance. The maximum of emf.
between the plates of the condenser is less each time the condenser
is discharged, and thus the oscillations of the current die away.
A good analogy to damped electrical oscQlations in a circuit is
found in the vibrations of a flat spring, clamped at one end in a vise,
and then bent to one side and released. Fig. 149. The spring
vibrates from side to side with decreasing amplitude, until finally
it comes to rest in its unbent position 0. When the spring is bent,
energy is stored up in it — the energy of bending. On being released
RADIO COMMUNICATION. 205
the spring moves and gains energy of motion, while the energy of
bending decreases. If there were no friction, the loss of one kind
of energy would be just offset by the gain of the other kind and the
sum total would remain constant. The spring would move past the
natural undisturbed position 0, under the influence of its energy of
motion, and would be brought to rest at a position just as far to the
other side of as was the starting point.
Friction has, however, the effect of opposing the motion and caus-
ing a dissipation of energy in heat, and each excursion away from
the resting point is smaller than the one preceding.
Free oscillations, then, can take place in a circuit containing in-
ductance and capacitance. These would be undamped in the ideal
case where the resistance can be regarded as zero. In all practical
cases of free oscillations, however, the oscillations are damped. To
produce undamped waves it is necessary to provide some source of
power to make good the energy dissipated in the oscillating circuit.
Strictly speaking, undamped free oscillations are impossible in
actual circuits. It is of importance to study the effect of the resist-
ance in determining the rapidity with which the oscillations die
away.
116. Frequency, Damping, and Decrement of Free Oscillations. —
If the resistance of the oscillating circuit is constant, it is possible to
calculate the period of the free oscillations in the circuit and to find
the rate at which the oscillations die away. If L, C and R are,
respectively^ the inductance, capacitance, and resistance of the cir-
cuit, then free oscillations in the circuit will have the frequency
^=2i'\L(
LC 41.2
JR2
(78)
This is known as the *' natural frequency" of the circuit. Similar
considerations apply to the pendulum and vibrating spring discussed
above. Each vibrates in a period natural to it, which depends upon
the dimensions, material of the vibrating system, and the friction
against. which it moves.
If it snould happen, in any case, that the quantity j^-^ is equal
to or greater than -jr-p tnen free oscillations in the circuit are impos-
sible; the current in the circuit does not reverse its direction at all,
but simply dies away. The circuit is said to be in the ** aperiodic '*
206 RADIO COMMUNICATION.
condition, that is, without period. Seldom do such cases occur in
radio circuits. Usually, the quantity .i^a instead of being larger
than j-^ is very small in comparison with the latter. We may there-
fore as a rule, use without error as the expression for the natural period
which is the same expression as for the frequency of the applied emf .
necessary in order that the circuit shall be in the resonance condi-
tion.
The rapidity with which the oscillations die away depends, not
only on the resistance of the circuit, but on the inductance also.
The greater the resistance and the smaller the inductance, the more
lapid is the damping and the rate at which the oscillations decrease.
If the resistance, capacitance, and inductance of the circuit have
£xed values, it may be shown that each successive maximum of
current is the same fraxition of the preceding maximum, as the latter
is of the maximum immediately preceding it. If, for example, the
second maximum is 0.9 of the first, the third will be 0.9 of the second,
etc. However, instead of adopting as a numerical measure of the
rate of decrease, this ratio itself, it is found more convenient iq the
mathematical theory of damping to adopt the natural logarithm of
the ratio of any maximum to the next following maximum with the
current in the same direction, i. e., the logarithm of the ratio of two
miaxima one cycle apart. This number is known as the ' ' logarithmic
decrement," or "decrement," for short.
In cases where the resistance of the circuit is not exceedingly laiige,
the decrement is equal to ir times the quotient of the resistance by
the inductive reactance of the circuit, calculated for the natural
frequency of the circuit. That is, the decrement is equal to x f o"// ) *
so that increasing the resistance or decreasing the inductance, both
increase the decrement. The natural frequency being practically
independent of the resistance, that is, equation (79) being suffi-
ciently accurate, the capacitive reactance is equal to the inductive
reactance. Thus the decrement is tt times the quotient of the resist-
ance by the capacitive reactance at the natural frequency of the
circuit.
RADIO COMMUNICATION. 207
Eocamples of Decrements. — Fig. 148 gives a graphic idea of the
dissipation of the oscillations in three cases where the decrements are
0.01, 0.1, and 1. These correspond to circuits of very small damping,
moderate damping, and excessive damping, respectively. Each
curve starts from the same ,value of current at the first maximum,
and for each the natural period of the circuit is the same. The
latter is represented by the horizontal distance, AB, BC, etc., in
each. The difference between the curves is striking. In the case of a
decrement of 0.01, the oscillations decrease only very gradually; this
case approximates that of undamped waves. In the extreme case of
a decrement of 1, the oscillations become negligible after only four
or five periods. To construct such curves the following simple
method may be used.
Assume a certain number of divisions in the horizontal direction to
represent the period of the oscillations, for example, five. Then the
curve must cross the horizontal axis every two and one-half divisions.
Choose a convenient number of divisions to represent* the first maxi-
mum of the current, for example, ten. The curves DE (Fig. 148) are
next drawn to scale, starting with the chosen value for the first maxi-
mum. The curves DE have the property that the height of the curve
falls off by equal fractions of its value for equal horizontal intervals.
^os instance, if the decrement is 0.1, we find, since 0.1 is the nat-
ural logarithm of 1.105, that the first maximum OD in the positive
direction is 1.105 times as great as the next, PG^ and so on for any
two successive maxima in the same direction. If, therefore, we
take 0I>= 10 division, PG will equal Y\(^~^'^^ division, RH will be
9 05
-I T/^g =8.19, etc. The oscillations must be confined between the
1.105 '
two curves DE^ and since the crossing points have also been located, as
as well as the positions of the maxima, it is not difficult to sketch in
the curve of oscillations free hand, making the loops of approximately
sine shape.
Number of Oscillations, — ^Although, strictly speaking, the oscilla-
tions never would become absolutely zero, they actually become
negligible after a certain time. A knowledge of the logarithmic de-
crement enables us to calculate how many complete oscillations will
be executed before their amplitude has fallen below a certain frac-
tion of the first oscillation. This number is greater the smaller the
decrement.
208 RADIO COMMUNICATION.
If, for example, we arbitrarily choose to find the number of
oscillations which will be completed before the maximum of current
will fall below 1 per cent of the value at the start, we have simply
to take the quotient of the natural logarithm of 100 by the decrement.
The natural logarithm of 100 is, near enough, 4.6. The number of
oscillations is thus 4.6 divided by the decrement. Thus in the three
cases given in Fig. 148 the numbers of complete oscillations will
be 460, 46 and 4.6, corresponding to the decrements 0.01, 0.1, and
1, respectively.
The maximum possible value of decrement would be infinite,
but the United States radio laws require that values greater than
0.2 shall not be used on account of the interference of highly damped
stations with other stations. The number of complete oscillations
calculated by the above rule is 23 for a decrement of 0.2.
The decrement gives an idea of the efficiency of a sending appa-
ratus. The smaller the decrement, the sharper the tuning possible,
and, therefore^ the greater the proportion of the emitted energy
which can be utilized in the receiving apparatus. The larger the
decrement the larger the proportion of energy which serves no
useful purpose, and which may cause serious disturbance to other
stations.
In the case of a spark circuit the idea of logarithmic decrement
is not exactly applicable. On account of the variable resistance
of the spark, the oscillations fall off according to a different law
than that just discussed. (See C. 74, p. 230.)
C. Resistance.
117. Resistance Ratio of Conductors. — ^When a steady emf. is
applied between the ends of a conductor, the current quickly rises
to the final Ohm's law value, and distributes itself uniformly over
the cross section of the wire. During the interval between the mo-
ment when the emf. is applied, and the moment of attainment of the
final steady state, the current distribution over the cross section is
not uniform. This effect is due to self-induced emfs. in the cross
section of the conductor. Suppose that a section be taken through
the axis of a cylindrical conductor and that the applied emf. tends
to produce a current in the direction of the arrow (Fig. 150). The
magnetic lines in the cross section will be circles, in planes at right
angles to the axis, and with their centers in the axis. In the figure,
the lines will be directed out of the paper in the region above the axis
RADIO COMMUNICATION. 209
and into the paper in the region below the axis. As the total cur-
rent rises in value, the number of lines of force through any portions
of the cross section, such as ABCD and EFGH, will be increasing,
and by Lenz's law (Sec. 45) this change of field will give rise to
induced emfs. which tend to oppose the changes of the field. The
directions of these induced emfs. will accordingly be those indicated
by the small arrows, and it is easy to see that the increase of the
current is aided in those portions of the cross section which lie near
the surface of the conductor, and hindered at the portions nearer the
axis. That is, the current reaches its final value later at the axis
of the cross section than at points on the surface of the wire. On
the other hand, if the circuit is broken after the distribution ot
current has reached the uniform state, the outer portions *of the
conductor will first be free from current.
These effects may be accurately described by the statement that
the current grows from the outer layers of the wire inward, and that
the current inside the conductor attains the same value as that at
the surface, only after a finite interval of time.
When a rapidly alternating emf. is impressed upon the conductor,
(a) the phase of the current inside the conductor lags behind that of
the current at the surface by an amount which is greater the nearer
the point is to the axis; and (6) the amplitude of the current is largest
at the surface and decreases as the axis is approached because
sufficient time has not been allowed for the final steady value to be
reached before the emf. was changed. This non-uniformity of current
distribution in the cross section is known as the "skin effect," and
it is equivalent to a reduction of the cross section of the conductor
with consequent increase in its resistance.
From these considerations, it will be seen that in addition to its
dependence on the frequency, the skin effect will be more serious,
the thicker the conductor and the greater the permeability and
conductivity of the material of which it is composed; for the thicker
the conductor, the longer the interval which must elapse before a
change in emf. will be felt at the center of the conductor and thus
tile greater the difference in the current density at different points
of the cross section. With given dimensions, the greater the per-
meability of the wire, the greater the emf. induced in its mass. The
better the conductivity, the less the ratio of the effective current
to the value at the surface.
97340"— 19 14
210 RADIO COMMUNICATION.
A numerical calculation of the magnitude of the skin effect can
be made only in a few special cases for which Circular 74, pages
299-308, should be consulted. Table 18 of Circular 74 will enable
one to see at a glance how great diameter of wire is allowable, in
order that the increase of resistance due to skin effect shall not
exceed 1 per cent of the direct current value. Such data are of
use in estimating the size of wire suitable for a hot wire ammeter,
in order that its resistance may not vary in the range of frequency
for which it is intended. For larger diameters of wire the effect
increases rapidly and cases where the high frequency resistance is
five to ten times the direct current value are not rare. These
facts must be kept in mind when estimating the current carrying
capacity of a conductor. The "resistance ratio'' is defined as the
ratio of resistance at the frequency in question to the resistance to
direct current. Then, for the same heating, the allowable current
at the high frequency will be less in the ratio of the square root
of the resistance ratio.
Since the skin effect tends to render useless for the carrying of
the current the inner portions of the cross section of a wire, thin tub-
ing, or a thin layer of good conducting material plated on the surface
of a poor conducting cylinder is a form of conductor suitable for
carrying currents of radio frequency. In fact, tubing which is very
thin in comparison with its radius has for the same cross section a
smaller high frequency resistance than any other single conductor.
To reduce the skin effect, a conductor is often built up of a number
of very fine conducting strands. The resistance ratio of such a
combination is, however, on account of the mutual inductance of
the strands, appreciably greater than the resistance ratio of one of
the strands. To be effective, the strands should be placed as far
apart as practicable, and the diameter of the individual strands
should not exceed about 0.1 mm. The most effective form of
stranded conductor, although expensive to make, is one where
the strands are so twisted as to form a woven tube. For further
particulars see pages 306-308, of Circular 74.
Effective Resistance. — The resistance of a circuit at high frequency
is never the same as the resistance measured by direct current.
To define what is meant by the resistance at high frequencies, we
have to divide the power lost in heating or otherwise dissipated, by
the square of the effective current. This quotient is known as the
*' effective resistance'* at the frequency in question.
RADIO COMMUNICATION. 211
The effective resistance of a circuit carrying currents of radio
frequency may be very appreciably affected by the presence of
neighboring conducting bodies. The energy of any eddy currents
which may be induced in the latter is drawn from the circuit in ques-
tion, whose effective resistance is thereby increased. On account
of the high frequency, this effect can be astonishingly large in good
conductors and may be appreciable in the presence of such a poor
conducting path as a painted surface.
Different portions of the same circuit should not be placed in
close proximity. The mutual effects of the currents which flow in
opposite directions in two parallel cylindrical wires is,, for example,
such as to cause the maximum current densities in the two cross
sections to be shifted to points nearer the other conductor, with an
increase in the effective resistance of each conductor above the value
it would possess in the absence of the other. In other tases (p. 302,
C. 74) the effective resistance may be reduced by the presence of
the other lead. An important example of the effect of the mutual
inductance of neighboring conductors on their effective resistances
is furnished by a system of parallel wires connected in parallel. In
this case more current, at radio frequencies, flows in the outer wires
than in the inner, and the differences may become very important.
This is a point which cannot be overlooked in the design of hot wire
ammeters to carry large currents.
118. Brus^, Spark, Dielectric, and Radiation Besistance. — ^As
has already been explained (Sees. 31 and 58), no dielectric is perfect.
Some heating takes place in it, and we may artificially represent a
condenser as equivalent to a pure capacitance in series with a
resistance. The introduction of a condenser into a radio circuit has
therefore the effect of increasing the effective resistance of the
circuit, and, except in especially designed air condensers, this effect
cannot be neglected. Care needs therefore to be taken that poor
dielectric materials be kept away from regions of intense electric
field.
When operating condensers at high voltages, large energy losses
may occur in the so-called brush discharge, and this effect will
generally give rise to a very considerable increase in the effective
resistance of the condenser.
If a spark gap is included in a circuit, the resistance of the spark
will have to be included in the total effective resistance of the
circuit. This spark resistance depends upon a number of circum-
stances, and the laws of its variation are very complex. In general.
212
RADIO COMMUNICATION.
a short spark gap has a larger conductivity per unit length than a
long one. Thus a series of short spark gaps is better than a single
one of the same length as the sum of the lengths of the shorter gaps.
The pressure and nature of the gas between the terminals also affect
the resistance which is materially decreased with reduction of
pressure. Further , the nature of the terminals and the constants of
the remainder of the circuit all affect the spark resistance.
Some of the power supplied to a circuit which is carrying a radio
current, is radiated from the circuit in the form of electromagnetic
waves (see Chap. 5). This may be regarded as the useful work
obtained from the circuit, and for transmission purposes the power
radiated should be made as large as possible, in comparison to the
power dissipated in the circuit itself, and in its immediate surround-
ings. The power radiated at any frequency is found to be propor-
tional to the square of the current flowing, so that the radiative
F»Q. 151
' (A) (b) (cl
Ty^Cft Off cou^lin^ ', (A) diroctcooj>lin^ (b) mdwotiva oowt>lin^
effect may be regarded, artificially, as causing a definite increase in
the effective resistance of the circuit. This fictitious resistance
increase is known as the "radiation resistance," and is found to be
directly proportional to the square of the frequency, or inversely
proportional to the square of the wave length.
D. Coupled Circuits.
119. Kinds of Coupling. — ^When two circuits have some part in
common, or are linked together through a magnetic or an electrostatic
field, they are said to be " coupled. " When the part in common is
an inductance (Fig. 151-a), the two portions of the circuit are said
to be "direct coupled.'* In Fig. 151-c the part in common is a
capacitance and this gives an example of "capacitive coupling."
In the important case in which the circuits are mutually inductive
RADIO COMMUNICATION. 213
(Fig. 151-b) the circuits are said to be "inductively coupled/'
More rarely the coupling is an "electrostatic" kind in which the
plates of a condenser in one circuit are placed between those of a
condenser in the other circuit.
It is customary to denote as the "primary" that circuit in which
the applied emf. is found, the other being regarded as the "sec-
ondary " circuit. When two circuits are coupled they react on one
another so that the current in each circuit is not the same as would
be the case were the other circuit absent. The extent of the re-
action is, however, very different in different cases. Circuits are
said to be "closely coupled" when any change in the current in
one is able to produce considerable effects in the other. When
either circuit is little affected by the other, the coupling is regarded
as "loose." The coupling between two inductively coupled cir-
cuits is made looser by increasing the distance between the two
coupling coils.
A more exact measure of the closeness of the coupling is given by
what is called the "coefficient of coupling" (denoted by k). Its
value in the case of direct coupling (Fig. 151-a) is given by
If the total inductances of the circuits in Fig. 151-b are denoted
by Li and X2> w© have for inductive coupling
and for capacitive coupling (Fig. 151-C),
As the coupling is made very loose, k approaches zero as its limit
for the closest possible coupling k would be unity.
The coupling of two direct coupled circuits may be increased by
increasing the amount of inductance which is common to the two
circuits, maintaining constant the total inductances (L^-\-M) and
(Lb-|- M) of the two circuits. To make the coupling of the induc-
tively coupled circuits closer, their mutual inductance is increased
by moving the coils nearer or by increasing the inductance of either
coil. For example, the coefficient of coupling of an antenna may
214 RADIO COMMUNICATION.
be increased by adding turns to the coil of the oscillation trans-
former, enough inductance being subtracted from the loading coil
to keep the total inductance of the circuit constant. Capacitive
coupling is closer, the smaller the common capacity Cm is in com-
parison with the capacities C^ and C^,
In some types of receiving apparatus the coupling condenser is
connected in a different manner from that shown in Fig. 151-c
(see Sec. 177), and in that case the coupling is loosened by a decrease
of capacitance in the coupling condenser.
The reaction of either circuit on the other affects, not only the
value of the currents in the coils, as would be expected, but has an
important influence on the frequency to which the circuits respond
most vigorously. This is explained in the following.
120. Double Hump Resonance Curve. — It may be shown (Sees.
16 to 18 of C. 74) that the reactance of either of the circuits, primary
or secondary, is zero, that is, the impedance is a minimum, for two
separate frequencies/'' and/'''', which are different from the natural
frequencies /i and /j, for which the primary and secondary circuits
are in resonance when taken alone. With loose coupling/^ and^^^
differ little from/i and/2. With closer coupling, however, the dif-
ferences become very appreciable. If /^ be used to denote the
lower of these two frequencies, then it may be shown that/^ is
always still lower than the lower of the two natural frequencies /
and /a, while the higher frequency /^^ is always higher than the
higher of the two natural frequencies. Increasing the closeness of
the coupling has always the effect of spreading /^ and /^^ further
apart. Furthermore, the difference between f^^ and the higher of
the two natural frequencies is always greater than the corresponding
difference between/'' and the lower of the natural frequencies.
These conclusions may be tested by means of a wavemeter. As
has been already pointed out (Sec. 112), the current induced in a
wavemeter circuit is a maximum when the wavemeter is tuned to
the frequency of the exciting current. Suppose the wavemeter to
be very loosely coupled to either the primary circuit or the sec-
ondary. Let the frequency of the current in the primary be varied
by small steps and adjust the setting of the wavemeter for each fre-
quency until the indicator shows a maximum current in the wave-
meter circuit. If the settings of the wavemeter condenser and the
corresponding deflections of the indicating instrument are plotted,
a resonance curve is obtained which will show two humps or peaks
corresponding to the frequencies /^ and f^^. The positions of the
RADIO COMMUNICATION. 215
two humps will be found to be different for a second resonance curve,
taken with a different coupling between the primary and the sec-
ondary. The coupling between the wavemeter circuit and the
circuit which is exciting it must be made as loose as practicable in
order that the wavemeter circuit may not react appreciably on the
other circuits and thus change their currents.
A more direct method of showing the two frequencies is furnished
by simply inserting a hot wire ammeter or thermocouple in the
circuit to be examined and noting the changes in its readings as the
frequency is continuously varied.
In the case of the usual coupled radio circuits, the two circuits,
primary and secondary, are adjusted independently to the same
natural frequency. That is, /i is made equal to /g. When the
coupling is made loose, hoihr/^ and /'''' approach the same value,
/^^ from above and f^ from below, and at very loose coupUng,
It might be supposed that in the special case where /i=/2, the cur-
rents in the circuits would be a maximum for a single frequence only,
namely, at the value of / to which they are both tuned. Never-
theless, both experiment and theory show that each circuit, even
in this case, offers a minimum impedance at two different fre-
quencies, just as is found for the more general case. The two fre-
quencies /^ and /^^ lie on either side of the value /, though not at
equal intervals from the latter, the difference/^^—/ being always
greater than/—/''.
When/i=/2, the effect of the coupling on the values of /^ and/^^
is shown by the simple relations
If the coupling is made more and more loose, the two frequencies
/^ and/'''' approach one another, and the two humps of the resonance
curves finally merge and become indistinguishable from a single
hump.
In the absence of a secondary current, there is no reaction on the
primary, which is no longer a coupled circuit, and will necessarily
be in resonance at a single frequency only (/by hypothesis). The
same remarks apply to the secondary when the primary circuit is
broken.
The further treatment of coupled circuits naturally follows two
different lines, according to whether the primary is excited by a
216 RADIO COMMUNICATION.
eine wave of a definite frequency (producing oscillations), or whether
the primary circuit is given a single impulse and then allowed to
oscillate freelv.
121. Forced Oscillations. — ^When a sine emf. of frequency / is
applied to the primary, the currents in the two circuits, primary and
secondary, are at first very complicated, consisting of oscillations
of the two frequencies /'' and /'''', superposed upon forced waves of
frequency/. The free oscillations quickly die away, and there re-
main sine currents of frequency /in both the primary and secondary.
High Frequency Transformer. — It can be shown that to obtain the
maximiun current in the secondary circuit, a certain value of the
coupling of the coils is necessary. If the coupling be made either
closer or looser than this value, the secondary current falls off in
value. In general, the proper coupling for maximum secondary
current will depend upon the resistances of the primary and sec-
ondary and their reactances, and can be determined better by actual
experiment than by calculation. For one important case, however,
the values of the coupling and the maximimi secondary current can
be expressed very simply.
If the primary and secondary circuits are separately tuned to the
frequency of the applied alternating emf. E, the maximum possible
E
secondary current has the value h^TTiW^ where Ri and iJj ^Je the
primary and secondary resistances. The value of the mutual induct-
ance (coupling) which gives the maximum secondary current may
be calculated from the relation 2ir/J/=V^i -^2* The primary current
E
under these circumstances assimies the value -fi=2P" which is
one-half the resonance value of the primary current when the sec-
ondary is absent.
These relations and the dependence of the secondary current on
the coupling are illustrated in Fig. 152, which shows the changes of
the secondary current as the mutual inductance between the coils
is varied. The resistances i2i=2.0 and i22=12.5 ohms are assumed,
and the secondary current is plotted in terms of its maximum value,
which is taken as 1. As abscissas are taken, not the mutual induct-
ance itself but 2ir/ Jf, so that the curve is applicable to different fre-
quencies, assuming, of course, that in every case the two circuits are
tuned to the frequency in question. Maximimi secondary ciurent
is, in this example, obtained for 27r/Jf=V2.0X 12^=5. Supposing,
RADIO COMMUNICATION.
217
for instance, that the frequency ia 100,000, the coils must be so placed
5
that their mutual inductance is o viQQ QOO * ^^ ^'^^ microhenries.
Current and Voltage Ratios. — The current ratio (secondary to pri-
mary) in the high frequency transformer, when adjusted to give
mn YiTniim current, has been shown to be -«/ o^, so that, in general, it
may be increased by decreasing the secondary resistance or by
increasing the primary resistance.
S 15
Zirf M
VAriAtioo oj secondary current with th« cou^Ii'n^
J
The voltage ratio is in general more complicated. If the two cur-
rents are tuned to one another and to the impressed frequency, the
voltage ratio (secondary to primary) approaches the value -U-tt 8^ the
resistances in the circuits are made smaller. If the circuits are not
tuned to the same frequency, but are closely coupled, the voltage
ratio approaches the ratio of the number of turns on the two coils
(when the resistance may be neglected), which is the case of the usual
alternating current transformer.
218 RADIO COMMUNICATION.
122. Free Oscillations of Coupled Circuits with Small Damping. —
Suppose the condenser in the primary circuit is given a charge, and
the primary circuit is closed directly or through a spark gap. If the
secondary circuit is open, the primary will oscillate freely, the fre-
quency of the current being given by the equation /i = _ ii^-rr > the
o
damping of the oscillations being determined by the ratio « }f~
as treated in Section 116.
As soon as the secondary is closed, the matter is complicated
by the reaction of each circuit upon the other. An emf . is induced
in the secondary by the changes of the primary current, and thereby
a forced oscillation is started in the secondary. The secondary
condenser is charged by this current and starts a free oscillation,
whose period will depend on the constants of the secondary circuit.
This latter wave will induce a forced oscillation in the primary,
and similarly the oscillation which was forced in the secondary
by the primary, will react on the primary, modifying the original
oscillation in the primary which produced it. The oscillations
in the primary will then further react on the secondary, and so on.
Naturally, the result will be very complicated, but it is evident
that each circuit is the seat of two waves, one free and the Other
forced by the other circuit. Each of the waves which we have
designated as free is, however, not entirely so, since it forces an
oscillation of its own frequency in the other circuit, and has to supply
the energy for this induced wave. This has the effect of modifying
the frequencies of these waves from the natural values /i and /j
already treated. Of the two waves in the primary, the free wave
has (with loose coupling) the greater amplitude, and the same is
true of the secondary except that here the amplitudes of the waves
are more nearly equal. With close coupling, the forced wave in
the primary becomes stronger, owing to the increased amplitude
of the secondary free wave. Finally, with very close coupling, those
waves predominate the frequency of which is/^. The frequency/'''
of the other waves lies so far above the natural frequency of either
circuit that only feeble oscillations of this frequency are present.
In general therefore the oscillations in both the primary and
secondary circuits are compounded of two damped oscillations of
different frequencies. It is of interest to study a little more closely
the nature of the complex oscillations resuting from the super-
RADIO COMMUNICATION.
219
position in a single circuit of the two oscillations of different fre-
quencies.
Damping Curves of Coupled Circuits, — Fig. 153 shows two sine
waves A and B of equal amplitudes but of different frequencies.
Curve C is obtained by taking the algebraic sum of the ordinates
of A and B. It is seen to be a curve the oscillations of which alter-
nately increase and die away. The frequency of these fluctua-
tions is equal to the difference of the frequencies of the components
A and B. The curve C passes through its zero values at nearly
regular intervals of time, excepting at those moments when the
resultant amplitude is passing through its minimum, when the
curve makes an additional passage through zero at the moment
the resultant maximum amplitude is zero. It is also noticeable
that the loops of the curve C are only approximately of sine shape.
An exactly analogous case is furnished by the resultant sound
wave coming from two tuning forks which are vibrating with some-
PlG IS»
Prsductjon of De*T»
what different frequencies. The sound which is heard alternately
increases and decreases in loudness, giving the phenomenon of
** beats." The number of beats per second is equal to the differ-
ence in frequencies of the two forks. Thus, if two forks have fre-
quencies of 259 and 255 vibrations per second, they combine to give
a sound which beats four times per second.
Free oscillations in coupled circuits are damped, so that in addi-
tion to the alternate waxing and waning of the resultant oscillation,
the energy of the oscillation as a whole dies away according to the
laws already treated in Section 116. Fig. 154 shows the nature
of the damped oscillations in the primary and secondary circuits.
The primary decrement is assumed to be 0.1 and that of the secondary
0.05. The two coexistent frequencies are supposed to have the
ratio of 4 to 5. The curve of oscillations is in each case drawn as a
full line. The dotted curves show the beating effect described
above, while the dashed curves give an indication of the damping
220 RADIO COMMUNICATION.
eSeot. It ie noticeable that the primary cunent is paamng throu^
its maximum values at the moments whea the secondary current
is Mro, and vice versa. Further when the primaryis passing through
a period of intense oscillation the secondary oacillatioos are small, etc.
Another important conclusion which can be drawn from Fig. 154
is that the energy of the coupled system is transmitted alternately
from the primary to the secondary, and back again from the second-
ary to the primary. Thus, at certain moments the energy is en-
tirely in the primary, at others entirely in the secondary, and at
other instants partly in the primary and partly in the secondary.
This transfer of enei^, first in one direction and then in the other,
shows that the primary and secondary play alternately the r6le of
driving circuit.
From the standpoint of radiation of energy, it is dedrable to hinder
the return of energy to the primary, after it has once been given to
the secondary. Since the closed primary circuit is of such a nature
as to radiate very little energy (see Sec. 136), no useful purpose is
served by the transfer of energy back to the primary, and some of
the energy thus handed back is necessarily lost in heating in the
primary. Further, the radiation of the energy of the secondary in
RADIO COMMUNICATION. 221
waves of two different frequencies is undesirable. The receiving
circuit can be tuned to give a maximum of current for either one of
the incoming wave frequencies, but not for both at the same time.
The partition of the radiated energy of the secondary in waves of
two frequencies is therefore wasteful, since only that wave to which
the receiving circuit is tuned is effective, while practically none of
the energy of the other wave is usefully employed, and it may cause
interference with other stations.
123. Impulse Excitation. Quenched Oap. — If by some means or
other, the energy of the primary circuit can be transferred to the
secondary and then all connection between the circuits can be re-
moved before any energy can be handed back to the primary, wo
may avoid the disadvantages just mentioned. In this case, the sec-
ondary will oscillate simply in its own natural frequency, and the
loss of energy in the primary can be restricted to the short interval
during which the primary is acting. By properly choosing the re-
sistance of the secondary, the damping of the radiated wave may be
kept small, and since only a single frequency is radiated, the advan-
tages of close tuning of the receiving circuit can be realized. Such
a method of excitation is known as "impulse excitation," and is
analogous to the mechanical case where a body is struck a single
sharp blow, and thereafter executes vibrations, the period of which
depends entirely on the inertia and elasticity constants of the body
itself, and not at all on the nature of the body from which the impulse
has emanated.
One means of obtaining an impulse excitation of the secondary is
to insert so much resistance in the primary that its current falls away
aperiodically (see Sec. 116). This has, however, the disadvantage
that considerable energy is lost in the primary due to the heating of
the rather large resistance of the primary by the initially rather large
primary current. A more satisfactory arrangement is the * ' quenched
gap." By dividing the spark gap in the primary into a number of
short gaps in series, the cooling effect of the relatively large amount
of metal is available for carrying away the heat of the spark dis-
charge. This is found to be sufficient, in the case of a properly de-
signed quenched gap, to prevent the reestablishment of a spark dis-
charge after the first passage of the primary oscillations through their
condition of maximum amplitude to zero , as at point D , Fig. 154. The
secondary, at this moment, is the seat of the whole of the energy of
the system and thereafter oscillates at the single frequency natural
222 RADIO COMMUNICATION.
to it. The dEimpingof the primary does not have to be made exceee-
ive, and the energy Icat in the primary ia restricted to the heating
during the short interval before the quenching of the primary oscil-
lations.
1%. 155 shows the fonn of the oscillations in the two circuits
for this case. The curvee are the same as in Pig. 154 up t« point D,
after which the secondary curve is a simple feebly damped oscilla-
tion. The construction and operation of the quenched gap are
treated further in Chapter 5, Section 156.
CHAPTER 4.
ELECTROMAGNETIC WAVES.
A. Wave Motion.
124. Three Ways of Transmitting^ Energy. — All of the ways of
signaling between distant places operate by one or by a combination
of these three methods:
(a) By a push or pull on something connecting the two places.
(b) By projectiles.
(c) By wave motion.
Thus think of all the ways in which you can arouse a dog asleep
at the other side of the room. You can prod him with a long stick
(method a). You can throw something at him; if you hit him it is a
case of method 6; if you miss him, the noise made when the missile
hits the wall or floor may wake him, in which case we have a com-
bination of methods b and c. You can whistle or call (method c).
You can flash a light in his eyes (method c). Any way that you can
think of is an example of one of these three methods. Of the three
methods the most important for our purpose is the third.
125. Properties of Wave Motion. — Everyone is familiar with
water waves. Many of their properties are common to all kinds of
waves. Thus the alternate crests and hollows, though invisible in
many types of waves are present in all. Examples of different
wave shapes are shown in Figs. 80 and 95, Chapters 1 and 2. The
simplest wave shape is the sine wave (Fig. 80).
Also, as in the case of water waves, all waves have a definite
wave length X, which is the distance between successive crests or
successive hollows. If we use the term phase to mean the position
at any time of a point on the wave outline, we can say that in general
the wave length is the distance between two successive points in
the same phase.
Furthermore, waves of all kinds travel with a definite velocity.
If one looks at a fixed point on the surface of a pool over which
ripples are moving, he can see that a crest appears at that point a
223
224 RADIO COMMUNICATION.
definite number of times in any given interval of time. The number
80 appearing in one second is called the frequency, /. If now the
frequency is multiplied by the length of one wave, we get the
distance moved by the waves in one second, which is the velocity, c,
or, in symbols, c=X/. The velocity of waves of different kinds is
very different in amount. Thus ripples on water travel with
velocities of from 10 to 100 cm. per second; for sound waves in air
the velocity is 330 meters per second; and the velocity of light and
electric waves is 300,000,000 meters per second.*
The more the surface of the water is displaced by the waves from
its position of rest, the greater is the amount of energy being passed
along. The amount of energy transmitted by water waves is con-
nected with the height of the crests and the depth of the troughs.
This also is true of all kinds of waves. The greatest displacement
from the position of rest that any point undergoes is called the
"amplitude" of the wave. Thus we say that the energy in wave
motion depends upon the amplitude. The amount of energy in the
wave depends on the work which has to be done to produce the
displacement. This is in general equal to the product of the resisting
force and the distance moved. Now in the case of many kinds of
waves, including electric waves, the resisting force is proportional
to the distance moved. Hence the work done and the energy
transmitted is proportional to the sqame of the amplitude of the
wave.
126. Wave Trains, Continaous and Discontinaoas. — If a stone is
dropped into a quiet pool of water, a "train*' of waves is started
which soon passes out from the starting point in all directions, leav-
ing the surface behind it undistiurbed. If a second stone is dropped
just at the moment that the siurface at the starting point has com-
pleted one up-and-down excursion, another wave train will start in
phase with the first, and the two will form one train. If the process
is repeated once after each complete vibration of the surface at the
starting point, continuous waves are produced. Similarly, if we
hold a vibrating body so that it touches the surface, continuous
waves are produced. By interrupting the vibration^ of the body,
we can produce interrupted or discontinuous trains of waves.
^Example.— VfhaX is the wave length of waves having a frequency of 100,000 cycles
per second which travel with a velocity of 300,000,000 meters per second.
c^300.060.000^ t^^
/ 100,000 ouwiuctwa.
RADIO COMMUNICATION. 226
Examples of these two kinds of wave trainfl are met with often.
Thus the sound from a musical instrument where the strings are
set in vibration by picking (as with a mandolin) is transmitted in
discontinuous trains, while that from an instrument whose strings
are bowed (as a violin) is transmitted by more nearly continuous
waves. Similarly, in radio we have to do with both kinds, contin-
uous waves being furnished by high frequency alternators, the
Poulsen arc, and the oscillating vacuum tube, while discontinuous
trains are given by condenser discharges in spark circuits. In
these latter the amplitude of the waves diminishes steadily in each
wave train; these are called "damped'* waves. Such waves are
discussed in Section 115.
B. Propagation of Waves.
127. Waves Propagated by Elastic Properties of Medium.^ — In
the case of ripples on the surface of water it is plain to the eye that
the waves are transmitted by the passing on of the up-and-down
motion of the surface at the soiurce. This is possible because at the
surface of the water the particles of the water are held together by
forces which resist their displacement. When one particle is dis-
placed, its neighbors are dragged with it to some extent. In tech-
nical terms, the medium of transmission is said to have "elastic"
properties and the forces brought into play are said to be elastic
forces. The velocity of the waves (ripples) depends on the nature
and amount of these elastic forces.
In the case of sound waves in air, we do not ordinarily see the
vibrations of the particles of the air. The vibrations are quite small
and the waves travel so fast that only under quite imusual conditions
can they be made visible. But the mechanism by which the energy
is transmitted is found to be of the same kind as in the case of water
ripples. By the delicate elastic connections between neighboring
portions of the air a vibration at one point is passed on to another.
Sound waves are of another type than water waves only because
the structure of air is different from that of water. Hence the elastic
reaction to displacement is different in the two media. This is the
sole cause of the differences between any two types of waves.
128. Properties of Electromagnetic Waves. — In the case of electro-
magnetic waves, often called "electric waves," the displacements
produced are of the kind already considered in the section on capaci-
1 For further explanation of the radiation of electric waves, see Starling, " Eleo-
tricity and Magnetism," pp. 423-429.
97340° — 19 15
226
RADIO COMMUNICATION.
tance (Sec. 23). The elastic reactions set up by such displacement
currents can be found by the same laws which determine the electric
and magnetic forces due to any current. It is beyond the scope of
this book to show the nature of these electrical elastic forces. It
will be sufficient, however, to state that they are such as to produce
waves in which (in free space) —
(a) The displacement (and the electric field intensity) are at
right angles to the direction of motion of the wave train.
(6) The magnetic field intensity resulting from the displacement
current is at right angles to the displacement and to the direction of
the wave train.
(c) The variations in the displacement (or the electric field inten-
sity) and the magnetic field intensity are in phase.
F\a. \s<:»
FlC3. »57
The «Iectric "field Artd tK« m^ncTic
■field AredT ri^hTdr^lea An<i tiTAvel
together.
ElecTnc lines of •force in A
charged ^late. condensor
(d) The velocity of the waves is 3 X 10* meters per second, the
same as the velocity of light.
These relations are shown in Fig. 156, where the curve marked
EotD shows the variations in the electric field intensity or displace-
ment, and that marked H the variations in the magnetic field inten-
sity, the wave moving in the direction shown by v.
129. Modification of Waves in Free Space Near the Earth. — Such
waves if started at a point in free space travel in all directions with
the same velocity. They may be modified in various ways as they
proceed. Thus, if they pass into a region of different dielectric
constant, they are in general changed slightly in direction and
partly reflected. Their energy is also absorbed to a greater or less
RADIO COMMUNICATION. 227
extent in their passage through any medium. This absorption is
greater for short than for long waves. In a perfect conductor no
waves could be transmitted, since in such a medium there is no
elastic opposition to the displacement of electricity. A perfectly
conducting sheet would reflect all of the wave energy falling on it.
However, a conductor parallel to the direction of motion of a wave
acts as a guide to the wave, through the action of currents induced
in it by the varying magnetic field of the wave. It takes less energy
from the waves, the better conductor it is. In the use of electric
waves in radio communication, all of these modifications occur and
serve to explain many of the irregularities of received signals. We
can think of the space through which radio signals are sent as being
bounded below by a sheet of varying conductivity (the earth's
surface) and above — at a distance of from 30 to 50 miles — ^by another
conducting region. This upper region where the air is much rarefied
is a fairly good conductor, owing to its ionization by radiations from
the sun. The region in between these conducting layers is usually
a good dielectric. Thus, this region acts more or less as a speaking
tube does for sound waves, though its action is much more compli-
cated. The electromagnetic waves are set up near the earth's
surface. They are partly transmitted as guided wave trains along
the earth's surface, modified by refractions and absorption at its
irregularities; another part, however, goes off as space waves, which
by reflections at the upper and lower layers of the conducting bound-
aries may recombine with the guided wave in such a way as either
to add or subtract their effects, depending on circumstances. In
the daytime the upper conducting boundary will be less definitely
marked than at night, on account of partial ionization of the air by
the sun's radiations. Hence, there will be less reflection of the space
wave in the daytime, and consequently the guided wave will pro-
duce the greater part of the effect at the receiving station. In the
night, however, when the upper boundary is more sharply defined,
there is more reflection of the space wave, and in general signals
received at night are stronger than in daytime. Night signals are,
however, more variable in intensity, particularly for short waves.
This is especially true during the time when the sunset line is passing
between two communicating stations. This is in general what we
should expect, as the upper boundary would be quite variable under
such circumstances. Clouds and other meteorological conditions
would cause great variations in the sharpness of this boundary sur-
228 RADIO COMMUNICATION.
face, and this may explain the rapid fluctuations in the strength of
received signals often observed.
From all these considerations it can be seen that the conditions
under which received signals will be most uniform in intensity are:
(a) Transmission using long waves.
(h) Transmission by daylight.
(c) Transmission over short distances.
(d) Transmission over uniform conducting surface of sea water.
It is onl> under these conditions that the performance of different
transmitting stations can be fairly compared.
130. Static. — The transmission of signals by electromagnetic
waves is often interfered with by stray waves and static charges called
"strays" or ** atmospherics," which give rise to variable currents in
the receiving antennas. These cause troublesome, interfering sounds
of a harsh, irregular nature in the radio receiver. These effects are
most frequent in summer and especially in a thunderstorm. They
are often very pronounced when a thunderstcrm is a few miles away.
They appear to be of two kinds; (a) chaises of electricity which come
from the surrounding atmosphere upon the antenna and then dis-
charge to ground producing a current; and (h) electromagnetic waves
which are produced by distant lightning or other electromagnetic
disturbance in the atmosphere. Strays are the worst enemy of radio
communication, especially in tropical countries. No satisfactory
method of eliminating them has been devised. They are much re-
duced by taking certain precautions. One is the use of loose coup-
ling between the receiving antenna and detecting circuit. Another
is the use of waves of zero or small decrement and receiving appara-
tus which can be very sharply tuned. The use of a musical note in
the transmitted signals also helps to overcome disturbance from strays.
Strays have been found in some cases to be reduced by using small
antennas or closed coil receiving aerials, with amplifiers.*
C. Theory of Production and Reception of Electromagnetic
Waves.
To produce a train of waves of any kind, a vibrating body is neces-
sary. The vibrations of this body have next to be communicated to a
continuous medium, after which the elastic properties of the medium
1 Information on strays and special methods of overcoming them is given in Flem-
ing, " Electric Wave Telegraphy and Telephony," 3d ed., pp. 774, 851, and Goldsmith,
"Radio Telephony," p. 220.
RADIO COMMUNICATION. 229
take care of the transmiflsion of the waves. In the case of electro-
magnetic waves the vibrating body is an oscillating electric charge
in a circuit (the sending antenna circuit), while the means by which,
these oscillations are communicated to free space can best be de-
scribed in terms of the motion of the lines of force which, when,
at rest, are used to picture the field about electric charges as in.
Fig. 53.
These lines are to be looked at as lines along which there is a dis-
placement of electricity against the elastic force of the mediimi.
Thus they cannot exist in conductors (in which no such elastic forces
exist). Under the action of the elastic forces the displaced elec-
tricity is continually urged to return to its position of rest. In other
words, there is a tension along the lines of force. In addition there
must be a pressure at right angles to the lines of force, otherwise those
lines would always be straight and parallel under the action of the
tensions. These pressures can be thought of as arising from the re-
pulsion between the displaced charges of the same sign in neighbor-
ing lines.
131. Magnetic Field Produced by Moving Lines of Electric Dis-
placement. — Consider what happens to the lines of force when a.
condenser is discharged. Before the discharge begins, the field is as.
shown in Fig. 157. Now, suppose a wire to replace the line abcj
thus discharging the condenser. The displacements previously
existing along abc vanish, or, in other words, the line shrinks to noth-
ing when the tension is relieved. But this, at the same time, does,
away with the sidewise pressure on the neighboring lines, which as.
the pressure from the lines outside of them still remains, move inward,
toward the wire under the action of this unbalanced pressure. Their
ends slide along the plates of the condenser during this motion and
when they come to the wire the displacements along their length
vanish. This process continues until all the lines have vanished
and the condenser is discharged.
Now, while this is happening to the electric lines of force in the
field, a current has been flowing in the condenser plates and the wire
abc; also the magnetic lines of force which always accompany any
current have sprung into existence and continue to exist as long aa
the current flows. In the space between the condenser plates, these
magnetic lines of force will be directed up from the plane of the paper
at right angles, both to the electric lines of force and to the direction,
of their motion. These two facts can be described in terms of the
230
RADIO COMMUNICATION.
motion of the lines by saying that the motion of the ends of the elec-
tric lines along a conductor causes a current to flow in it, while the
motion of the electric lines at right angles to their own length pro-
duces magnetic lines of force in the other direction, which is per-
pendicular to the direction of motion. If the motion of the electric
line is parallel to its length, there will be no magnetic field pro-
duced. From this point of view, what takes place in the medium
is the cause of what takes place in conductors. The energy in the
former (in the case we are considering) appears in the latter as heat.
132. Mechanism of Badiation from a Simple Oscillator.-^Now
consider what takes place when the discharge is oscillatory instead
of in one direction. To fix our ideas, let us take the case of the simple
FiO
Fid isd
electric fi«Ui at« nai4}iMN
0«eilUtor «t di ' f f a r iff momanf*
Hertzian oscillator, the electrostatic field of which, before the gap
becomes conducting, is shown in Fig. 158-a. (The field to the left
is shown by dotted lines, in order to be able to keep track of each
line clearly in its motion as shown in the following figures.) When
a spark passes and the gap becomes conducting, the electric line of
force ah vanishes and those from each side begin to move up under
the unbalanced sidewise pressure, as before. Here, however, when
the ends of the line ahc reach the gap, we must suppose that it has
sufficient momentum so that the ends cross and the middle portion
travels across the gap. After two lines have done this, the state of
things is as represented in Fig. 158-b. There will soon come a
different state of things, however, owing to the shape of the lines.
RADIO COMMUNICATION. 231
When tho ends get to the gap before the middle portion, as shown in
Fig. 158-c, they will cross as before, and soon thereafter we will have
the loop formed as in Fig. 158-d. Now, at some time as the ends
continue to go up, this loop will break, forming two parts m and n,
as shown in Fig. 158-e. This is because at that moment the angle
of intersection becomes so acute that each part of the line will be
moving parallel to its length, in which case neither half will have
any magnetic field and, consequently, no momentum to carry them
by each other. The process goes on as shown in Figs. 158-f , g, and
h, the last of which shows the state of things when one half oscillation
has been completed, and the charges on the oscillator have been
reversed in sign. A cylindrical sheet of lines of force has then been
detached from the oscillator and is traveling outward. At this
moment those lines left attached to the oscillator have been stretched
as far as their momentum can carry them, and they begin to con-
tract again and repeat the process, provided the gap is still conduct-
ing. In the next half wave length, another cylindrical sheet of lines
of force will be snapped off, so to speak, and the process will continue
until the energy lost as heat in the oscillator has exhausted the supply
of lines which remain attached to it. These cylindrical sheets, as
they spread out, become more and more nearly plane, the plane being
perpendicular to the motion away from the oscillator. During the
process shown in Figs. 158-b to 158-g, that is, while the current in
the oscillator is flowing upward, the motion of the electric lines of
force generate magnetic lines (not shown), which form circles around
the oscillator running into the paper to the right and coming out on
the left. These magnetic lines vanish at any point, when the electric
lines of the attached field come to rest as in Figs. 158-a or 158-h, but
continue with the moving electric lines of the radiated cylindrical
sheet. When the cylindrical sheets have moved so far that they can
be considered practically as planes, then the magnetic lines also lie
in these planes, but perpendicular to the electric lines and to the
direction of motion.
In the case of a simple vertical antenna, the mechanism of radia-
tion is quite similar. In this case, however, since the lower end
of the antenna is earthed, only the upper halves of the waves shown
in Figs. 158-a to 158-h are produced, so that the field looks like
that shown in Fig. 159, where the electric lines are shown in
elevation and the magnetic lines in plan, while in between is shown
the wave form common to both. At any one point in space, the
232 RADIO COMMUNICATION,
lines approach and separate like a bellows. When the wave has
progreaeed bo far that the lines can be regarded as sections of planes,
the Btate of things will be as Bhown in Fig. 160 for the electric
linee, while the same figure will also represent the magnetic lines
if rotated through 90° about the line ox. Where the surface over
which the waves travel is not a perfect conductor the ends of the
lines will be as shown in Fig. Idl.
The Bame method of picturing the process of wave production
applies to other forms of radiating systems of either the open antenna
or the cl(«ed coil type (see Sec. 151}. Inall forme loops are formed,
and detached in the aame general way. In some of them the dis-
tribution of the lines of force is such as to favor the production of
more such loops than in others: this means that such an antenna
win be a better radiator than the others.
133. Action In Becelving. — The mechanism of the reception of
VKvea by an antenna can be followed through in terms of the lines
RADIO COMMUNICATION. 233
of force in an analogoua mannet. Thus suppose the antenna to be
located with reepect to the incoming wave train as shown in Fig.
162. Then the upper ends of the linee as they arrive travel down
the antenna ae shown in the dotted lines and give rise to moving
charges of electricity in the antenna, or the receiving action can.
be thought of in another way. As the advancing waves sweep
across the receiving antenna the electric field intcnaity along the
antenna alternates in value. This is equivalent to an alternating
voltage between the top of the antenna and the ground, A still
difierent way of looking at the receiving action depends upon the
principle that an erof. is induced in a conductor whenever there ia
relative motion between the conductor and a m^netic field. The
moving wave has a mimetic field which sweeps past the antenna,
and thus there is relative motion between the antenna and this
magnetic field, which results in an emf. in the antenna. This
emf. ie what causes the received current in the antenna.
The reception of electromagnetic waves in a closed coil used
in place of an antenna can be explained by the same principles.
The explanation is somewhat difficult because of the diflerencea
of phase between those currents in diSerent parts of the coil. For
such antennas it is more convenient to think of the current as pro-
duced by the changing magnetic flux through the coil, due to the
alternations of the magnetic field associated with the wave. Either
way of looking at it leads to the same result.
234 RADIO COMMUNICATION.
D. Transmission Formulae.
134. Statement of Formulae. — ^When the general ideas of wave
production and reception discussed above are put into exact mathe-
matical language, it is possible to deduce certain practically useful
formulae connecting the currents in the sending and receiving
antennae, their heights, resistances, and distance apart. While it
is beyond the scope of this book to derive them, they are given
without proof to aid the student in gaining an idea of the magnitude
of the effects to be expected at various distances and with different
types of antennae. In the formulae which follow h stands for the
height of an antenna or coil, I for current, X for wave length, d for
the distance apart of the two antennae or coil aerials, while the
subscripts s and r refer to the sending and receiving ends, respec-
tively. R stands for the resistance of the receiving circuit. All
lengths are supposed to be in meters.
If the waves are sent out by a simple flat top antenna and received
on a similar one, we have
^'■" R\d ^ ^
If the waves are sent out by a simple antenna and received on q.
closed coil, we have
j_UMh,^lJfJ, (84)
ZvA U
where l^ is the length of the receiving coil and iV, the number of
turns of wire with which it is wound.
If the waves are sent out by a closed coil and received on a simple
antenna, we have
1184^, I K N, I. ,«-.
^' Sx^5 ^^^
where l^ is the length of the sending coil and N^ the number of tuma
of wire with which it is wound.
If the waves are sent out by a closed coil and received on a similar
one, we have
Ir- J^^ (86)
In all of these formulae, if d is greater than 100 kilometers, they
must be multiplied by the factor e— 0.000047 -t^ in order to get
RADIO COMMUNICATION. 235
more accurate results. (Both d and X are in meters, and 6 is equal
to 2.718.)
135. Examples of TTse. — To illustrate the use of the fonnulae
suppose it is desired to know how much current must be put into a
plain antenna 20 meters high sending a 300-meter wave, in order that
the current in a similar antenna 50 km. away shall be detectable
easily with a crystal detector (that is, shall be about 1/10,000 amp.),
the resistance of the receiving antenna being 10 ohms.
Solving the first equation for J^, we have:
R\dl, _ 10X300X50,000XTi>i^ _ 1 aporoximatelv
"''•-188 K K 188X20X20 5^^* ^pproxmiately.
As another example, suppose that the receiving antenna, in the
first example, is replaced by a square coil of 2 ohms resistance, having
sides 2 meters long and wound with 10 turns of wire. If the sending
current is \ amp. as before, what will be the current in the receiving
coil? Using the second formula
WMKKUN^I^ 1184X20X2X2X10Xi ^■,,.,^,
■*'"" R>:'d " 2X300X300X50,000 ""^-^/^"^^^P-
For a current of this size it would be best to use a simple vacuum
tube receiver instead of a crystal detector.
As a third example, suppose the sending aerial to consist of a single
square turn of wire 10 meters on a side, in which the current is \ amp.
at X=1000 meters. With how many turns should a square coil
2 meters on a side and having a resistance of 5 ohms be wound to
receive at a distance of 50 km., if a vacuum tube which can detect
a current of 1/10^ amp. is used? Solving the fourth equation for JV,
we have
y R>?d T , 5XWX5XWX1/10« ,, ^,
-^'-7450 K h K It N, i,-7450XlOXlOX2X2XlXi-^^^^^^^^^^-
136. General Deductions. — ^From the formulae certain general
conclusions can b e drawn . Thus since X appears in the denominator,
it follows that, for given heights of antennae, sending current, re-
ceiver resistance, and distance apart, there will be more current in
the receiver, the shorter the wave length used. On the other hand,
there is more absorption of short waves than long ones, as was stated
when we were considering the modifications that free waves undergo
(Sec. 129). This effect is taken account of in the correction factor
236 RADIO COMMUNICATION.
to be used for large distances. In this factor, X enters in such a way
as to make the received current less when the wave length is short
than when it is long. Hence, in general, we conclude that to get
the greatest possible received current, we should use short waves
for short distances and long waves for long distances.
It may be seen from the formulae that, for simple antennae, the
received current (for a given wave length, sending current, receiver
resistance, and distance apart) is greater, the greater the heighto of
the antennae. In the case of closed-coil aerials under the same con-
ditions, the received current is greater the larger the areas and the
number of turns of the coils. For the dimensions actually used,
antennae are much more effective radiators and receivers than
closed coils. In order to secure the same radiation or received
current with a closed coil as with an antenna, other conditions being
the same, its dimensions must be made nearly as great as the antenna
height. However, it is often possible to put more current into a
transmitting coil than into the corresponding antenna, and also the
resistance of a receiving coil is usually smaller than that of the cor-
responding receiving antenna. Hence the closed coil can be a
smaller structure than the antenna.
The closed coil has some other advantages. For a given pow^er
input in the transmitter, the closed coil aerial is not at quite such a
disadvantage with the ordinary antenna as the formulae show,
because a larger fraction of the radiation is sent out in the direction
desired. As a receiver, the closed coil has the very great advanta^re
that the direction of the waves it receives can be determined.
These points are discussed further in the next chapter.
E. Device for Radiating and Receiving Waves.
137. Description of the Antenna. — ^The antenna is used in radio
communication for two purposes, (1) to radiate electric waves, and
( 2) to receive or detect electric waves which come to it. An antenna
consists essentially of one or more wires, suspended at some elevation
above the earth. When electric waves reach an antenna, they set
up an alternating emf . between the wires and the ground, and the
longer and higher the wires, the greater the emf. produced. As a
result of this emf., an alternating current will flow in the antenna
wires. The energy of the current is absorbed from the passing
wave, just as some of the energy of a water wave is used up in causing
vibrations in a slender reed which stands in its way.
RADIO COMMUNICATION. 237
A receiving antenna needs to be large, in order to gather in enough.
energy from the electric waves to affect the receivins apparatua.
LikewiBeasending antenna needs to have large dimensions, in order
to send electric waves to a greater distance. The same antenna is
often used for both sending and receivu^. An a
receiving only may, however, be made simpler than one which ia
also required for sending purposes.
The simplest form of antenna would be a plate P, Fg. 163, sup-
ported above the earth and insulated from it, except for the connec-
238 RADIO COMMUNICATION.
tion through the wire PT, called the * * lead-in wire "or * * lead-in . " The
plate and the earth form the two terminals of a condenser, the space
between them furnishing the dielectric. When an alternating emf .
is introduced into the wire, charging currents flow into and out of P
and the earth, the dielectric being strained first in one direction and
then in the other. As has been explained in the previous chapter,
these strains are equivalent to displacement currents of electricity
through the dielectric, which serves to complete the circuit. A region
in which the dielectric is undergoing alternating strains ]& the start-
ing point of electric waves. The larger the plate and the higher it
is raised from the earth, the greater the amount of space in which
this strained condition exists, and the more powerful the waves
which are radiated.
In practice, wires are used for an antenna instead of plates. A
single vertical wire is, for its size, the best radiator, but it has to be
made extremely long in order to get sufficient capacitance for long
wave or long distance work (Section 142). Antennae of different
numbers of horizontal or inclined wires instead are, however,
practicable and radiate very well. It must be thoroughly under-
stood that an antenna is merely a large condenser and may have
various shapes consistent with this condition, although some forms
will radiate electric waves much better than others.
138. Different Types.* — ^The umbrella type of antenna, Fig. 164,
consists of a number of wires which diverge from the top of a mast,
and are attached to anchors in the ground through insulators, -4, as
shown in the figure. Lead-in wires L are brought down from the
junction of the wires B to the apparatus. The jwrtions of wire BA
take the place of the plate P of Fig. 163. This antenna may be
erected quickly, and is used for radio pack sets.
An antenna of horizontal parallel wires, supported between two
masts and insulated therefrom, is common. This is the standard
form for ship stations. According as the lead-in wires are attached
at the end of the horizontal wires (Fig. 165) or at their center (Fig. 166)
the antenna is said to be of the inverted L or of the T type. The V
antenna consists of two sets of horizontal or slightly inclined wires,
supported by three masts, so that the horizontal portions form an
angle, Fig. 167.
For short distance sending, simpler antennae may be used, such
as, for example, a simple wire supported between two stakes at a
height of only a few feet from the ground. For emergencies, a long
1 See also S. C. Radio Pamphlet No. 2.
RADIO COMMUNICATION.
239
insulated wire may be laid upon dry ground, the apparatus being
inserted at the middle, forming what is known as a "ground an-
tenna." For receiving stations equipped with amplifiers or other
delicate receiving apparatus, very simple antennae may be employed,
even for long-distance work.
139. Current and Voltage Distribution in an Antenna. — ^When an
emf . is introduced into an antenna, a charging current flows in the
wires as was described in the ideal case of Fig. 163. If we attempt
to form a picture of this process in the wire antenna, we must remem-
ber that every inch of the wire forms a little condenser, with the earth
acting as the other plate. The antenna is said to have a distributed
capacitance.
As the electricity flows from the bottom of the antenna, some of it
accumulates on each portion A of the wire, causing a displacement
FlQ. I<i&
FlO.!«i9
\
•
\
1
\
«l
"^0
1
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^n
v>
«v
•5»
>\
'^'i
\
1
\
1
\
1
Za
>rTh ■
FlQ . no ArwaloXY ^ Antenna i
V I bwiti& .afrii^i. tff«2r
,\ )\c mofr«n.Ur>|e force
^ ,' ', Vatj^ motion , &mal I fon»
\ '
V »«io motion , Ur^ ^orc«
Dia^Ucem*nT currents
from An Antftnn*
Distribution oj^ current
and voll42je alon^an
antenna
ktocurrerjt'
lAr^ Vol
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^nkt
na»nt
.corjQjn
vo
kJoeOrrcnt
Ur^VBlt;^
Lai^eormnT
Uo^JTa^e
llo current
current through the dielectric to earth, as shown in AB (Fig. 168).
The current in the wire accordingly diminishes as the free end F of
the antenna is approached, and becomes zero at that end. The cur-
rent is evidently different at different parts of the antenna, being
zero at the free end and a maximum where the antenna is connected
to the ground (Fig. 169). This is in marked contrast to the case of a
direct current, which always has the same value at every point of the
circuit. The difference here is brought about by the very high
frequency of the currents.
The voltage of the antenna, on the contrary, is zero at the grounded
end and has a maximum value at the free end. In fact, the latter is
the point where the most intense sparks can be drawn off; therefore
the insulation of the antenna from nearby objects and the earth must
be particularly good at this point. (In Fig. 169 the voltage and cur-
240 RADIO COMMUNICATION.
rent are supposed to be measured by the horizontal distance frotn the
solid vertical line.)
A large capacitance to earth, concentrated at any point of the
antenna, causes a large change in the current at that part of the an-
tenna. If this bunched capacitance is located at the top of the
antenna, such as is the case with a flat topped antenna of long wires,
with only a few vertical lead-in wires, the average current in the
flat top portion will be large, and it increases slightly in strength as
the charges pass down through the lead-in wire (picking up the
charges there), hence giving a large current through the receiving
apparatus. It is a distinct advantage to have aa large a part of the
total capacitance of the antenna as possible at the top.
140. Action of the Ground. Counterpoises. — ^The electric oscilla-
tions in an antenna may be regarded as somewhat analogous to the
vibrations of a string, stretched between two points A and Bj and
plucked at the middle, C, in Fig. 170. The stretching forces on the
string are greatest at the points A and J5, while the portion Cis under
very small force. The motion of the string is niost considerable at C,
while the points A and B do not move. If we regard current as
similar to motion and voltage to force, we can see (according to state-
ment in the preceding section) that the top of the antenna resembles
in its behavior the end A (or B) of the string, while the bottom of the
antenna corresponds to the point C of the string.
The part played by the earth may now be understood. If we
suppose for a moment that the antenna is disconnected from the
ground and insulated, then the lower free end would become a point
where the current would be zero and where the variations of voltage
would be large (corresponding to point B, Fig. 170). The portion
where the ciurent would be a maximum would lie at some elevated
point. To set a string in vibration requires the smallest force when
it is plucked at the middle. Right at the ends it is almost impossible
to set it in vibration. Just so, the antenna, if disconnected from
earth, would be almost impossible to set in vibration if the emf . were
applied at the bottom end. For successful working, the exciting
apparatus would have to be joined to inaccessible points of the wire
higher up. It is necessary, then, to make sure that the lower end of
the antenna is a region where a current is large, and with a good
ground this condition is satisfied.
In places where the ground has poor conductivity (dry, rocky
soil, with ground water at some considerable depth) it becomes diffi-
cult to satisfy the above condition. In such cases an earth capaci-
RADIO COMMUNICATION.
241
tance or * * counterpoise " must be used. This is merely an insulated
mass of metal M of large extent (Fig. 171) placed near the ground.
The lower end of the antenna is joined to the metal which forms the
upper plate of a condenser, while the more moist layers W of the
earth, deep below the surface, form the lower plate. As far as the
antenna is concerned, the counterpoise takes the place of the ground.
The antenna can, therefore, be excited by suitable apparatus placed
in the antenna, or coupled to it just above M or near the ground.
(The connecting of the generating apparatus to the antenna is
treated in Sec. 160.) In some cases, a netting of wires placed near
the earth is used as a counterpoise, in others, insulated wires are car-
ried from the base of the antenna and laid out upon the ground.
In airplane radio outfits a counterpoise must necessarily be used.
This is furnished by the metal wires of the framework, the engine,
fio.ni
Fi<a iTz.
^
^
Fl<3. 113
riorth
y
/
\ tJorfh
/ N
\
TTinci^ic o^ the
C o u rrter )3P I de
Variation of th«.
Lffectiv. ^eaiatance ^i TriAr^uUtN
of an AntennA
llluAtnktir\5 Mettiec
ten
stay wires, metallized wings, etc. The antenna proper consists of a
weighted wire let down from the airplane, which trails behind when
in flight. A reel allows this to be coiled up when a landing is to
be made. On airplanes the antenna is below the coimterpoise, but
the action is not different from the ordinary antenna and counter-
poise systems.
F. Antenna Characteristics.
The behavior of an antenna depends upon its capacitance, in-
ductance, and effective resistance just as is the case with any oscil-
lating circuit. The capacitance and inductance determine the
length of the radiated waves (see Sec. 116) ; the resistance determines
the damping.
973400—19 16
242 RADIO COMMUNICATION.
141. Capacitance. — ^The energy which can be given to a con-
denser, when it is charged to a voltage Ej is equal to one-half the
capacitance, C, multiplied by the square of the voltage. The
energy which is supplied to an antenna each second when it receives
N charges per second is, therefore (as given in Sec. 34),
P=^ CIPN
We may, evidently, increase the supply of power to an antenna by
increasing the number of charges per second, or by raising the voltage.
It is not practicable to raise the rate of charging beyond about
1000 to 1500 sparks per second. The voltage on tHe antenna can-
not be made greater than about 50,000 volts without loss of power
through leakage and brush discharges. The only remaining factor
which can be varied is C in the above formula; therefore, a high
power sending antenna must have a large capacitance. Large
capacitance means many wires of great length; that is, a large and
costly structure.
The capacitance of a single wire parallel to the ground can be cal-
culated approximately, as also the capacitance of certain simple
arrangements of parallel wires (see C. 74, pp. 237-242). Even in the
simplest cases, however, the presence of houses, trees and other
neighboring objects, and the difficulty of allowing for the lead-in
wire, makes any precise calculation impossible. It should be noted,
however, that the capacitance of a wire is proportional to its length.
The capacitance of two wires near together is less than the sum of
their capacitances, and, in general, although each added wire adds
something to the capacitance, it adds much less than the capacitance
it would have alone in the same position. As an indication of what
values of antenna capacitance may be expected, the following values
may be cited:
Airplane and small amateur antennae, about 0.0005 mfd.
Ship antennae, 0.0007 to 0.0015 mfd.
Large land station antennae, 0.005 to 0.015 mfd.
That is, in spite of their size and extent, antennae do not possess
greater capacitance than is foimd in ordinary variable air condensers
(see Sec. 32).
The capacitance of an antenna is easily measured by a substitu-
tion method (L. W. Austin). The wire from the antenna and that
from the ground are connected to an inductance coil of such value
as to give a wave length five or more times the fundamental (Sec.
RADIO COMMUNICATION. 243
144). A generating circuit is loosely coupled to this and varied to
resonance. The connections to antenna and ground are then re-
moved from the inductance coil and replaced by a variable con-
denser, which is then varied to resonance. The condenser setting
gives the antenna capacitance. This is subject to a small correc-
tion for the antenna inductance, which, however, may usually be
neglected.
142. Inductance. — ^Although principal stress has been laid upon
the conception of the antenna as a condenser, the inductance which
its wires necessarily possess is of equal importance in determining
the wave length of the radiated waves. The antenna is, in fact, an
oscillating circuit, and as such the wave length or frequency of free
oscillation depends upon the product of the inductance and capaci-
tance. See formula (79), Section 116.
The inductance in general is not large — 50 to 100 microhenries is
a common range of values — but larger capacitance is necessarily
associated with larger inductance, so that high-power antennae are
naturally long wave antennae. Methods for measuring inductance
and capacitance of antennae are described in C. 74, pp. 79, 83 to
86, and 98. Antenna inductance is more conunonly obtained from
a combination of measurements of capacitance and wave length.
143. Besistance. — ^The wires of an antenna offer resistance to the
current, which is greater for the high frequency antenna current
than it would be for a steady current, on account of the skin effect
(see Sec. 117). In addition to this, the radiation of energy in waves
causes a further increase in the apparent resistance of the antenna.
The ** effective resistance of the antenna" is defined as the quotient
of the power given to the antenna by the square of the antenna cur-
rent. That is, if R IB the effective resistance, the total power put
into the antenna is RPj where / is measured at the base of the
antenna. The effective resistance is different for different fre-
quencies, as is shown below.
The total power is dissipated in the following ways, (1) as heat in
the antenna wires and earth connection, (2) brush discharge, (3)
leakage over or through insulators, (4) heat in the dielectric sur-
rounding the antenna, and in any condensers that are in the antenna
circuit, and (5) radiated waves. Part of (5) will also be turned into
useless heat by inducing eddy currents in near-by conductors, such
as guy wires or metal masts. If R^I^ represents all the power except
that radiated, and R^^I^ represents the power radiated as waves,
244 RADIO COMMUNICATION.
then it is evident that R'I^-\-R'T=^R P, or R'+R''=R, the effec-
tive resistance. R^^ is called the ** radiation resistance." It might
bo defined as that resistance which, if placed at the base of the
antenna, would cause as great a disaipation of energy as the energy
radiated in waves. It will be different at different frequencies.
It gives an idea of the radiating power of the antenna for each
ampere of antenna current.
When the effective resistance of an antenna is measured at a
number of frequencies and the results are plotted, a curve is ob-
tained like curve 4, Fig. 172. The shape of the curve is explained
by considering the laws according to which the different kinds of
resistance in the antenna vary with the wave length. The radia-
tion resistance decreases as the square of the wave length increases.
Such a variation is represented by curve 1, Fig. 172. The resist-
ance of the conductors and earth connection is nearly constant with
different wave lengths, curve 2. The dielectric resistance increases
nearly as the wave length, curve 3. Curve 4 is the sum of curves
1, 2, 3. If the losses in the dielectric are very small the curve does
not have a minimum, as at ^, but becomes horizontal at the right
end. If these are negligible, the curve merely falls toward a lim-
iting value.
To reduce the dielectric losses no portion of the antenna should
be in contact with buildings or trees. To reduce eddy current
losses care should be taken to have the antenna a reasonable distance
from guy wires, and especially large masses of metal. Guy wires
may be cut up and insulated in sections. On shipboard, induced
currents are produced in iron stacks and guy wires near the antenna,
and in cases where the frequency of the waves agree with the natural
frequency of oscillation of these metal objects, considerable power
losses may result. These show themselves, when they are present,
as humps on the experimental curve 4, Fig. 172, at the frequencies
in question.
The effective resistance of an antenna is often as high as 20 to 30
ohms at the fundamental wave length. The minimum value may
be 5 to 10 ohms for a land station and as low as 2 ohms for a ship
station.
144. Wave Length, and Its Measurement. — ^The wave length of
the waves emitted by an antenna, when no added inductance or
capacitance is inserted in the antenna circuit, is known as its " funda-
mental wave length." Byputtinginductance coils (''loading coils")
in the antenna circuit, longer waves may be radiated, while on the
RADIO COMMUNICATION. 245
contrary, capacitances put in series with the antenna enables it to
produce shorter waves than the fundamental. The use of a series
condenser is avoided where possible, since it has the effect of decreas-
ing the total capacitance of the antenna circuit (Capacitances in
Series, Sec. 35) and thereby diminishing the amount of power which
can be given to the antenna. The addition of some inductance has
a beneficial effect, since the decrement of the antenna ia thereby
lessened and a sharper wave results. It is not advisable to load the
antenna with a very great inductance, however, as it is not an effi-
cient radiator of waves. The waves emitted are very much longer
than the fundamental wave length. As a general rule, small send-
ing stations, for short ranges, work best on short waves, and long-
distance stations on long waves. Long waves have the advantage
for long-distance work that they are not absorbed in traveling long
distances to the extent that short waves are.
The United States radio laws specify that high-power stations shall
use waves longer than 1600 meters, that the Navy has the range
from 1600 to 600 meters, that ship stations shall transmit on a wave
length of 300, 450, or 600 meters, while amateurs, when permitted to
work, must confine themselves to waves shorter than 200 meters.
The majority of high power stations use waves longer than 3000
meters, and 10,000 to 15,000 meters are used by some.^
Measurement of Antenna Wave Length. — For a simple vertical wire
grounded antenna the fundamental wave length is slightly greater
than four times the length of the wire. The constant is often used
as 4.2, and applies approximately also to flat top antennas (L or T
types) with vertical lead-in wire, the total length being measured
from the transmitting apparatus up the lead-in wire and over to the
end of the flat top. It is usually easier, and certainly more accurate,
to measure the wave length radiated from an antenna directly by
the use of a wavemeter. (Sec. 112.) The wavemeter coil needs
merely to be brought somewhere near the antenna or lead-in wire
and the condenser of the wavemeter adjusted to give maximum cur-
rent in the wavemeter indicator. The wave length corresponding:
to the wavemeter setting is then the length of the waves radiated
1 It appears likely that in the future the legally prescribed values will be changed.
Possibly the range of from 200 to 2000 meters will be reserved for land stations,
except for a small range around 600 meters for airplanes, while ship stations will be
required to use 2000 to 6000 meters, and above this limit high power stations will
work.
246 RADIO COMMUNICATION.
hy the antenna. If the loading coil and series condenser are cut
out, the measured wave length is the "fundamental wave length"
of the antenna.
145. Harmonics of Wave Length. — ^A simple radio circuit has a
reactance equal to zero at a single frequency, namely, the resonance
frequency, and the maximum current possible with the given emf.
will then flow. This result is strictly true only when the capaci-
tance and inductance are concentrated at definite points of the cir-
cuit. In an antenna, however, the inductance and capacitance are
distributed, and it is found that a maximum of current is obtained
ior a whole series of different frequencies or wave lengths.
What is called the "fundamental frequency" is the lowest fre-
quency for which the current attains a maximum, when not loaded
with either capacitance or inductance. Denoting this by/, there
are in the same antenna other resonance frequencies 3/, 5/, 7/, etc.,
called the "harmonic frequencies" of the antenna. With the usual
methods of producing current in an antenna it radiates principally
waves of its fundamental frequency alone; free oscillations of the
liarmonic wave lengths are almost entirely lacking. However, when
-emfs. having the harmonic frequencies are applied, vigorous oedl-
laticns of those frequencies may be set up.
146. Directional Effect. — It is desirable, for certain purposes,
that the energy of a transmitting antenna may be sent in a particular
direction. The range of a station may thus be increased and inter-
ierence decreased. Still more important is the ability of an antenna
ix) receive waves coming from a single direction, but to offer no
response to waves from other directions. This is valuable as an
•effective means of reducing interference, since in general the inter-
fering station is not likely to lie in the same direction as that with
i^rhich it is desired to communicate.
A further and very important application of antennse with direc-
tional characteristics is the possibility of triangulation. If C, Fig^.
173, is a transmitting station, and the waves come in to station A
from a direction which makes an angle x with the north, while at
station B waves from C arrive from the direction BC, which makes
an angle y with the north, then the positions of the stations -4, J5, C
•can be calculated, provided only that the distance AB and the
angles x and y are known. If C is an enemy station, it may be lo-
cated by measurements of its direction, as observed from receiving
stations A and B whose positions are known. Or, if C is supposed
RADIO COMMUNICATION. 247
to be a lighthouse station, which is radiating signals, a vessel can
determine its unknown position A, even in a fog, by observing the
direction of C, and then after sailing a known distance AB, maldng
similar radio observations of the direction of C from its new position
B. The positions A and B and the ship's course can be worked out.
Even in clear weather it is often desirable to have a means of check-
ing up astronomical observations of the ship's position, since a small
error of observation may have serious consequences when a vessel
is near the coast.
All forms of unsymmetrical antennse, such as the inverted L and
the F, are somewhat directional in their characteristics, at least on
land. The so-called ground antennse give considerably better trans-
mission along their length than at right angles. Closed coil aerials
have, however, shown themselves particularly adapted to this liind
of work. Further details are given in Sections 151, 152 below.
G. Antenna Construction.
147. Towers and Supports. — ^For land stations wooden masts
have been much employed. For portable antennae these are made
in sections which fit together like a fishing rod. For higher power
stations, latticed metal masts are common, and in some cases, tubular
metal masts in telescoping sections. Except in special instances,
guy ropes or wires are necessary, and in some cases the support is
slistained entirely by these. It has been quite generally regarded
as a structural advantage to allow a small freedom of movement to
the mast, so that it may rock slightly in the wind. A simple one-
wire antenna may be held by any support that is available. When
a tree is used to support either end, a rope should run out for some
distance from the tree, and the wire be attached to this by an insu-
lator, so that the antenna wire itself may not be in or near the tree.
The standard fiat top ship antenna makes use of the ship's masts for
supports. The antenna wires are stretched between two booms or
spreaders from which halyards run to the masts.
148. Insnlators. — ^The insulation of an antenna is a matter re-
quiring careful attention. The system depicted in Fig. 174 is typ-
ical of a ship's antenna. In the case of the antennae for large land
stations, the guy ropes are interrupted by insulators. Porcelain,
hard rubber, or electrose rods into which eyebolts are molded are
common. A form of nearly spherical porcelain insulator, so grooved
as to carry the two wires firmly without their coming in contact, is
248
) COMMUNICATION.
] insulator breakup, the
shown in Fig. 175. In the event of t
wires do not part.
Where the lead-in wires from the antenna paaa through the walls
cd the house in which the sending and receiving apparatus is in-
stalled, special care needs to be taken to ensure good ineulatiou. A
form much used for this purpose is shown in Fig. 176. In the case
of some large aerials, the supporting mast itself has to be insulated
from the ground at its base. The design of an insulator which com-
bines sufficient mechanical strei^h with good dielectric properties
is a difficult matter.
149. Antenna Switch. Conduotors. — An antenna switch is a ne-
cesaity in all permanent installations. This has the function of dis-
connecting the receivii^ apparatus from the antenna completely.
RADIO COMMUNICATION, 249
when a message is to be sent, and vice versa. The action of such a
switch is made such that it is impossible for the operator to make a
mistake and impress the large sending voltage upon the delicate re-
ceiving apparatus. Since the currents in the antenna wires have a
high frequency, the resistance at radio frequencies is larger than at
ordinary low frequencies. (See Sec. 117.) Phosphor bronze wires
of seven or more strands are commonly used.
150. Gronnds and Counterpoises. — To obtain a good conducting
ground connection is a comparatively easy matter in a ship station.
In a steel ship, a wire is merely attached to the hull of the ship and
the good conductivity of the sea water assures an intimate connec-
tion with the ground. On a wooden ship, a large plate of metal is
attached to the outside of the hull, under water, and the ground
wire is connected to it.
The ground connections of some. land stations are often very elab-
orate, a considerable number of copper plates or heavy wires, ar-
ranged radially from the foot of the antenna, being buried in moist
earth. In general, the endeavor is made to insure a considerable
area of conducting material in contact with the moist earth. Coun-
terpoises are especially useful when the soil is dry and rocky, or
when time is not available for making a ground connection. The
counterpoise may consist of a considerable area of wire netting, sup-
ported parallel to the ground, or laid upon it; or insulated wires may
be carried radially from the foot of the antenna, being held at a short
distance from the ground. The amount of wire used in the counter-
poise should be as much as, or more than, that used in the antenna
proper. The antenna should always be grounded through a special
switch, when not in use, to avoid possible damage from lightning.
H. Oosed Coil Aerials.
Although closed circuits are by no means as powerful radiators or
receivers of electric waves as the usual forms of antenna, they possess
strong directional characteristics, and are used in installations where
this property is especially desired. An inverted L antenna is very
common when it is desired to transmit in a single chosen direction,
but for directional receiving, the closed coil is universally used.
The relative strength of signal obtainable with antennae and closed
coils may be calculated from the transmission formulfle given in
Section 134.
250 RADIO COMMUNICATION.
The problem of confining the radiated waves to a limited range
of directions has not, however, been very satisfactorily solved.
There is a marked tendency for the wave front to become spherical
as the wave travels forward, and thus lose the form it had in the
vicinity of the radiator.
A much more important consideration is the location of the
direction from which waves come to the receiving station, and for
this the action of an aerial consisting of a flat coil of few turns is very
successful.
151. Directional Curve. — Fig. 177 gives a graphical idea of the
variation of the received current in the coil when its plane is revolved
80 as to make different angles with the direction of the incoming
waves. In the figure, the direction of the incoming waves is along
the line AB. If OA represents the received current when the plane
of the coil is along this direction, then the effect of rotating the coil,
80 that its plane stands in the direction MN, is to reduce the received
current from OA to ON. When the plane of the coil makes a right
angle with the direction of waves, the line MN would become
tangent to both circles and the distance ON would become zero.
No current should then be received when the plane of the coil is at
right angles to the direction of the incoming waves. From the sym-
metry of the diagram, it is clear, however, that the received current
should be the same for two positions of the coil at 180*^ with one
another, for example, OA and OB, or OJV^and OM. Usually, how-
ever, there are other considerations that enable the operator to
determine in which of the two possible directions the transmitting
station lies.
To make a determination of direction, the closed coil aerial,
standing with its plane vertical, is connected to a variable condenser
to form a closed oscillating circuit. The circuit is tuned by means
of the condenser, to the wave length of the incoming wave. A suit-
able detecting circuit is connected to the terminals of the condenser.
A horizontal graduated circle is provided to identify the position
of the plane of the coil. The coil is then rotated on its vertical axis,
until tiie signals disappear. There will usually be a certain range
of angular positions of the coil for which no response will be obtained
in the detector. This is easily explained by Fig. 177. If the
radius of the circle, drawn with as a center, represents the smallest
received current which causes a noticeable effect in the detecting
RADIO COMMUNICATION.
251
circuit, then it is evident that for positions of the coil lying within
the angles COD and EOF, no signal can be received.
To determine the direction of the waves, the positions C and D
are noted on the graduated scale, for which the signals just disappear
and just become audible, respectively, and then the coil is turned
about 180** and the two similar positions E and F are sought. By
taking the average of the circle readiirgs at C and B, and E and F,
that position of the coil may be determined which lies at right angles
with the desired direction. The instrument is set up at the start,
80 that the scale reading will give directly the direction of the waves
in degrees from the north and south line.
With proper design, it is possible to determine the direction of a
sending station to within 1° or 2° of the correct value. To
obtain such accuracy, however, one must be careful that no masses
Fio. m
Direefiorw^! ch«Mct'cn.stic
ef clefted c6»\ aerMi!
Fi<3. n&
Fia.n9
I
PUT 5|>iral AerMi
— -Hl-c—
of iron, or other metal, or any object which is capable of distorting
the wave front lies in the vicinity of the coil. Neglect of this pre-
caution may give rise to determinations of direction which may be
easily as much as 15° in error, and, in the case of very short waves,
even worse. Where a mass of metal has a fixed position relative to
the radio apparatus, for instance the engine in an airplane, the set
may be so calibrated as to eliminate the error which the engine
would otherwise cause in the direction indicated.
152. Constants of Closed Coil Aerials. — It is found that the
maximum received current in a closed-coil aerial is greater, the
larger the number of turns of wire on the coil, the greater the area
of the coil, and the greater its inductance. The current varies
inversely as the resistance and the square of the wave length. For-
252 RADIO COMMUNICATION.
mulae for the current received in terms of current in the distant
transmitting aerial are given in Section 134.
It would seem at first sight that the increase in resistance, due to
increasing the number of turns and their area, would be offset by
the rapid increase of the inductance with the number of turns and
the area of the coil. The resistance to high frequency currents is,
however, dependent on the wave length and increases rapidly as
the latter approaches the value of the fundamental wave length of
the coil. The fundamental wave len^h of a coil aerial is that which
is radiated by the coil when no capacitance is present in the circuit
except that between the turns of the coil itself (Sec. 114.) Com-
pare with Sec. 145. As a guiding rule it may be stated that a closed
coil aerial should not be used to receive waves which are shorter
than about two or three times the fundamental wave length. That
is, to receive short waves a coil of small inductance and capacitance
should be used. Such a coil must have few turns. To receive
longer waves, coils of a larger number of turns may be used. Experi-
ence shows that best results are obtained with one or two turns
embracing a large area for use with short waves, and for long waves,
coils with 20 to 30 turns, not so large in area.
For convenience of construction, squafe coils are found to be the
most suitable. The wire may be woimd in a flat spiral. Fig. 178,
or on the surface of a square prism, Fig. 179. Flat spirals of only
a few turns are used, since the inner turns rapidly become less
useful as the area diminishes. The spacing of the wires is determined
by the allowable capacitance of the coil.
The capacitance of a coil of given dimensions increases with the
number of turns, at first rapidly, and then more slowly. With the
wires close together, the capacitance is a maximum and grows
rapidly less when the wires are separated, until a certain critical
spacing is reached, beyond which the capacitance changes very
slowly.
For a square coil 8 ft. on a side, the wires should be placed at
least 0.35 in. apart; for one 4 ft. square, 0.2 in.; and for a 2 ft. coil,
J^ in. Increasing the distance between the wires decreases the
inductance of the coil; at the same time it reduces the capacitance.
However, it is foimd that, for a given length of wire, properly spaced
as just indicated, the fimdamental wave length of the coil ia about
the same with different dimensions. This fact is illustrated in the
following table, where 96 ft. of wire are used in each case.
RADIO COMMUNICATION.
253
Characteristics of Closed Coil Aerials.
Length
of a side
of the
sauare
(feet;.
Number
of
turns.
Spacing
of
wires
(inch).
Tnductanco
(microhenries).
Capacitance
(micro-mfd.)
Funda-
mental
wave
length
(meters).
S
6
4
3
3
4
6
8
1
96
124
154
193
75
66
55
49
160
170
174
183
These coils should be used with a condenser of sufficient capaci-
tance to bring them into resonance at 500 to 600 meters. The first
coil would be most suitable for these wave lengths, on account of
its small high frequency resistance, and greater effective area.
The range of coil stations when used with field sending sets is,
of course, short. When used to receive powerful stations, however,
surprisingly good results have been obtained. Thus the great
European transatlantic stations have been heard in Washington
with coil aerials such as have been described, using vacuum tube
amplifiers. An instance is on record where all the great European
stations were received in France by a coil aerial only 18 cm. square,
having 200 turns.
CHAPTER 5.
APPARATUS FOR TRANSMISSION AND RECEPTION
(Exclusive of Vacuum Tubes.)
A. Apparatus for Damped Wave Transmission.
153. Function of Transmitting Apparatus. — Electric waves, by
means of which radio communication is carried on, are produced by
the transmitting apparatus. Power must be supplied by some kind
of electric generator; this must be converted into high frequency
currents which flow in the transmitting aerial and cause electric
waves which travel out through space. The waves may be un-
damped or damped. Damped waves consist of groups or trains of
oscillations repeated at regular intervals, the amplitude of the oscil-
lations in each train decreasing continuously. The number of these
trains of waves per second is some audible frequency. When such
waves strike a receiving apparatus (described later), they cause a
tone in the telephone receiver. Signals are produced by means of
a sending key, which lets the trains of waves go on for a short length
of time (producing a dot) or a longer time (producing a dash).
The principles of damped and of undamped waves are the same
in many respects, so that much of what is told regarding damped
wave apparatus applies to undamped waves as well. Particular at-
tention is first given to damped waves, as the apparatus is simple
and easily adjusted, and is suitable for portable sets and for short-
distance communication.
154. Simple Spark Discharge Apparatus. — Damped oscillations are
produced when a condenser discharges in a circuit containing induc-
tance. The condenser is discharged by placing it in series with a
spark gap and applying a voltage to it high enough to break down or
spark across the gap. As explained in Section 115, the oscillations
produced when the condenser discharges in such a circuit are
damped and soon die out. Methods of producing a regular succes-
sion of such condenser discharges are explained in the following. A
high voltage must be applied to the condenser at regular intervals.
This is done by the use of a transformer. Through the primary of
the transformer is passed either an alternating current or a current
254
RADIO COMMUNICATION.
255
r^ularly interrupted by a vibrator operated by the transtonner
(induction coil). For the use of the induction coil, as in radio
trench seta, see Section 157. The principle is beet studied first in
the altematii^ current method.
In Fig. 180, P and S are the primary and eecondary of a Btep-up
tranefonner (Section 58), which receivee power from an a.c. gener-
ator. The primary may be wound for 110 volts, and the secondary
for 5000 to 20,000 volts. By means of the transformer the condenser
C is charged to a high voltage, and stores up energy. 'W'hen Hie
voltage becomes great enough it breaks down the spark gap and the
discharge takes place as an oscillatory current in the inductance
coil L and its leads. See Section IIS. The main discharge does not
take place through the turns of S on af'count of its relatively high
impedance. The transformer is sometimes still further protected
from the condenser discbarge by inserting choke coils (not shown
in Fig. 180) in the leads between the transformer and condenser.
These obstruct the high frequency current, but do not hinder the
passage of the low frequency charging current into the condenser.
Fig. 181 shows a transformer used in radio sets.
The standard generator frequency is 500 cycles per second. This
causes the condenser to disehaige 1000 times a second, once for
each positive and n^iative maximum if the spark gap is of such
length as to break down at the maximum voltage given by the trans-
former. The number of sparks per second is called the "spark
frequency." With the standard spark frequency of 1000 per
second the amount of power the set sends out is considerably greater
266 RADIO COMMUNICATION.
than it would be at a low irequency like 60 cycles per second, be-
cause the transmitted radio waves are more nearly continuous, as
will be shown later. The radiated wave trains strike a receiving
antenna more frequently and their amplitude does not need tj> be bo
great to produce tiie same effect as stronger wavee received at longer
intervals of time. The higher frequency produces a tone in the
receiving telephone that is more easily heard, because the ear is
most sensitive to sound waves of about 1000 per second and also
the tone is more easily heard through atmoephBic disturbances.
F:o. li!l.— Slep-up transformer [or charglag rondenser.
A 60-cycle supply may be used if the number of sparks per second is
increased by using a rotary spark gap giving several sparks per cycle.
See Section 156.
Each condenser discharge produces a train of oscillations in the
circuit, and each train of oscillations consists of alternations of cur-
rent which grow less and less in amplitude. This is illustrated in
Fig. 192, and the comparative lei^ths of the trains of oscillatioiw and
the lapse of time between their occurrence are discussed in Section
ICO.
RADIO COMMUNICATION. 257
155. Transmittiiig Condensers. — Before discussing the means of
getting the oscillations into an antenna (Section 160), the appa-
ratus used in generating the oscillations will be described in detail.
The most common types of condensers used in radio transmitting
circuits use mica or glass as the dielectric, with tinfoil or thin copper
as the conducting coatings. Compressed air and oil condensers are
sometimes used, but are bulky. For very high voltages the con-
denser plates are immersed in oil to prevent brush discharge. For
moderate voltages a coating of paraffin over glass jars, especially at
the edges of the metal foil, will satisfactorily reduce brush discharge.
For calculation of the size of transmitting condenser needed see
Section 170.
156. Spark Gaps. — ^When the gap is broken down by the high
voltage it becomes a conductor, and readily allows the oscillations
of the condenser discharge to pass. During the interval between
discharges the gap cools off and quickly (see Section 160 and Fig.
193) becomes non-conducting again. If the gap did not resume its
non-conducting condition, the condenser would not charge again,
since it would be short circuited by the gap, and further oscillations
could not be produced. The restoration of the non-conducting state
is called "quenching." A device called the ** quenched gap"
for very rapid quenching of the spark is described below in this
section. Additional appliances for the prevention of arcing are
discussed in Section 167.
Plain Gap. — A plain spark gap usually consists of two metal rods
so arranged that their distance apart is closely adjustable. See
Fig. 182. It is important that the gap be kept cool or it will arc;
for that reason the sparking surfaces should be ample. Often the
electrodes have fins for radiating away the heat. An air blast across
the gap will greatly aid the recharging by removing the ionized air,
to which the conducting power of the gap is due. At the sparking
surfaces an oxide slowly forms which being easily removed in the
case of zinc or magnesium, is not very troublesome. With other
metals in general the oxidation is serious and is rapid enough to
make operation unstable and inconvenient.
With a given condenser, the quantity of electricity stored on the
plates at each charging is proportional to the voltage impressed
(Section 30), and this can be regulated by lengthening or shortening
the spark gap to obtain a higher or lower voltage at the beginning
97340°-_i9 17
258
RADIO COMMUNICATION.
of the discharge. The length of the gap which can be employed is
limited by the voltage that the transformer is capable of producing,
the ability of the condenser dielectric to withstand the voltage,
and the fact that for readable signals the spark discharge must be
regular. If the gap is too long, sparks will not pass, or only at
irregular intervals. The condenser is endangered also. If the gap
is too short it may arc and burn the electrodes. Arcing causes a
short circuit of the transformer, and the heavy current that flows
interferes with the high frequency oscillations. An arc gives a
yellowish color and is easily distinguished from the bluish white,
snappy sparks of normal operation. Even if no arc takes place.
Fia. 182
Plain -Df>ArK C<^p
the voltage is reduced by using too short a gap and this results in
reduced power and range. The length for smooth operation can
usually be determined by trial.
Quenched Gap. — It is found that a short spark between cool elec-
trodes is quenched very quickly, the air becoming non-conducting
almost immediately after it is broken down, or as soon as the current
falls to a low value. This action is also improved, if the sparking
chamber is air tight. The standard form of quenched gap consists
of a nimiber of flat, copper or silver discs of large surface, say 7 cm.
to 10 cm. in diameter at the sparking surface, wjth their faces sepa-
rated by about 0.2 mm. To provide the necessary total length of
RADIO COMMUNICATION. 259
gap for high voltage charging, a number of theso small gaps are
put in series, so that the spark must jump them all, one after the
other. The discs are separated by rings of mica or paper, see Fig.
183. Fig. 184 shows a commercial type of quenched gap. The
motor-driven blower attached serves to keep the discs cool. They
are usually made with projecting fins for radiating the heat, and in
one design air spaces are provided between the pairs of discs which
form the successive gaps. The number of gaps is determined by
the voltage, allowing about 1200 volts for each gap. Eight or ten
gaps are usually sufficient.
The quenched gap is not used in sets having a supply frequency
as low as GO cycles per second. The sparks obtained at that fre-
quency are found to be irregular and not of good tone. For this
case a rotary gap is used, as explained below. For 500-cycle supply
the quenched gap is adjusted to break down at the maximum value
of the applied voltage; that is, with its total length so adjusted as
to give one spark for each half cycle of the emf. See Fig. 185.
Discharges at other times are not possible, and as a result of this
regularity a clear note is obtained. This quenched gap is con-
sidered as standard for power up to about 10 kw. One advantage
of the quenched gap not previously explained, is that it aids the
production of a so-called pure wave. This is discussed in Section
163. It has also the advantage of being noiseless, on account of the
very short gaps and the enclosure of the spark.
Rotary Gap. — ^A rotary gap consists of a wheel with projecting
points or knobs, with a stationary electrode on each side of the wheel.
See Fig. 186. The spark jumps from one stationary electrode to one
of the moving points, flows across the wheel, and then, after leaping
the corresponding gap on the other side, passes out at the second sta-
tionary electrode. The number of sparks per second is thus deter-
miaed by the speed of the wheel which is motor driven so that signals
of high pitch can be produced. For a modified form of rotary gap
see Fig. 187. An advantage of the rotary gap is its prevention of
arcing, because of its motion and the fanning action, and because
the electrodes brought successively up to the spark gap have time
to cool in their idle intervals.
In the case of a * 'synchronous " rotary gap the speed is so main-
tained as to bring the knobs near together at just the moment when
the alternating voltage upon the condenser reaches its maximum
value, positive and negative. Thus 500 cycles will produce 1000
RADIO COMMUNICATION.
RADIO COMMUNICATION.
Bparks a second. This regular occurrence of the diachargea gives
Bmooth and efficient operation, and a pure musical tone. The
eynchrosizing is made possible by attaching the rotating element
ot the spark gap to the shaft of the generator which chai^ee the con-
denser. A rotary gap not so timed is called "non-synchronous, "
Attempts to produce a high pit<h from a 60-cycle source by a
synchronous gap giving, say, exactly 6 sparks per half cycle, have
not given satisfaction, because the applied voltage is not the same
at the time of the different sparks, and while the note is of high
fiC. 186.
Rotary Spark Cap
pitch, it is not musical. It has been found better fo useanon-
BynchronouB gap in such a case, producing a large number of sparks
per second and letting them occur wherever they may happen
262
RADIO COMMUKICATION.
during the cycle. The irregularities will somewhat baJance up.
While the tone ia not strictly mueical, it can be made of high pitch.
The non -synchronous gap ie best used if nothing but a 60-cycle or
other low frequency source is available. Such a low frequency,
however, is being avoided in modern apparatus. The standard
frequency is 500 cycles per second at present, although there ia a
decided tendency toward the adoption of 900 cycles per second.
The plain spark gap is not now used except in small sets; quenched
or rotary gaps are the rule. The plain gap cannot bo properly de-
ionized to allow the condenser to rechaige, and it is very difficult, or
impossible, to prevent arcing when large power is used, especially
with a large number of sparks per second, as in modem practice. As
regards the choice between the quenched and rotary gaps the rotary
Fia. 187
does not find favor because it ia very noisy. Another objection to
the rotary gap, for use on airplanes, is that when the gap is driven
by aemall airfan, the lone given by the radio transmitter varies with
every change of speed or direction of the airplane.
157. Simple Induction Coll Set. — For short distance communica-
tion in trenches, and in general for power below J kw., it is common
to use an induction coil or a power buzzer instead of an alternator
and transformer, to charge the condenser. The wiring of an induc-
tion coil is shown in Fig. 188. P is the primary coil of a tew turns
{heavy lines); S ie the secondary of many turns of fine wire; JisaQ
iron core magnetized by the primary current; and H ia a. piece of
soft iron at the end of a spring forming a sort of vibrating hammer;
Ji ia an adjusting screw for the vibrator; C is a condenser of a few
RADIO COMMUNICATION. 263
microfarads shunted around the vibrator points to prevent their
burning. The vibrator points may be replaced when necessary by
drilling a hole and driving in a piece of silver. F shows the vibrator
points where the primary current is made and broken in rapid
succession as long as the key K is closed. When current flows, H
is first attracted, breaking the current at V after which the spring
causes it to return to its first position, remaking the current. The
action is then repeated. The frequency of operation depends upon
the mass of the hammer H and the stiffness and length of the spring.
It is similar in that respect to an electric bell. This piece of ap-
paratus is really an open core transformer, the changes of current
being produced by the automatic interrupter or vibrator, which is
operated by the magnetism of the core. The source of power is
usually a storage battery of 8 to 20 volts. Owing to the changes of
primary current, rapid changes of magnetic flux occur and produce
a high voltage in the large number of turns of the secondary coil.
Referring again to Fig. 180, consider the induction coil put in
place of the a.c. transformer. When the coil is put into operation,
with its secondary terminals connected to the condenser and dis-
charge circuit, a continuous stream of sparks will pass across the
spark gap as long as the key is pressed.
158. Operation of Induction Coils from Power Lines. — Fairly large
power induction coil sets are used as emergency transmitters on
ships. These employ batteries, so as to be independent of the
ship's generator. On land, however, when a battery is not avail-
able, it is possible to operate an induction coil from a d.c. 110-volt
power line by inserting a rheostat in series. In this case, it is
absolutely necessary to shunt the transmitting key with a condenser
similar to the vibrator condenser, or else a serious arc at the key will
take place at the first attempt to signal, and the ciurent will not be
broken when the key is released. Of course, the method of insert-
ing a rheostat is very wasteful, as the RP loss in the rheostat is large,
much greater in fact, than the power actually used in the radio
apparatus.
A scheme to avoid a voltage as high as the 110 volts across the
break at the key is to use a voltage divider consisting of two rheostats
in series, as in Fig. 189. Suppose the spark coil has 2 ohms resistance
in the primary, and requires 10 volts to operate it. If one rheostat
is set at 10 ohms and the other at 2 ohms, with the induction coil
and key in a shunt around the 2-ohm coil, then the voltage applied
264
RADIO COMMUNICATION.
to the induction coil will be 10 volts with the key closed. Note
that the voltaga across the key when open is 18.3 volts.
With a.c. supply the methods are different. One method of oper-
ating an induction coil from 110 volts a.c. is to use a small, step-
down transformer to reduce the voltage to an equivalent battery
voltage. This requires no series resistance or reactance, and is a
fairly efficient method. Induction coils are sometimes operated on
110- volt a.c. power lines by insertion of a series reactance. The
vibrator in the primary circuit is not necessary if the supply is 500-
cycle, and it is preferable to clamp it permanently in the closed
position. The set then becomes similar to Fig. 180. Induction
coils may have the primary wound for 110 volts, in which case no
transformer nor series reactance or resistance is needed.
159. Portable Transmitting Sets. — For portable sets, or for Army
field use the simplest apparatus for short distances is a small induc-
iioVo\U<ic:
A^AAAA/VVs/V"-®!^ AAAAAr
PiQ. M
Induction coil on
d-c. f9ow«.r li'ne .
(^scorvdAry circuit
not 5hewn}
<4)
1^
Coil
TofirrvS"
Fia. HO
ih
-c C
Power bwtf*^r ci'rcoit
tion coil set, operated from a storage battery. A plain spark gap
may be used, for simplicity, but the use of a quenched gap will
usually improve the operation. When fairly long distances are to
be covered it is advisable to replace the induction coil by a small
step-up transformer. A source of alternating current then takes the
place of the battery. For a small set this source may be a generator
which is driven by hand through gearing. For larger power the gen-
erator may be driven by the engine of a motorcycle or some other
gasoline engine.
For short distance work the condenser may be charged and radio
oscillations produced, without an induction coil, by the use of a
power buzzer and a storage battery or a few dry cells. See Fig. 190.
The buzzer is shown at Z . The more voltage applied to it the greater
RADIO COMMUNICATION. 265
is the charge given to the condenser C. When the vibrator arm is
at the right in the diagram, the condenser discharges through the
inductance L. This forms the closed oscillating circuit. The con-
denser should be comparatively small; the apparatus is limited to
short wave lengths.
For very short distances the more common military practice is to
use "ground telegraphy" or "T.P.S.*' {tSUgraphie par sol) in-
stead of radio. For the theory and practical application of ground
tel^raphy, which uses no wires between the two points of commu-
nication, see Radio Pamphlets Nos. 10, 15, and 18.
160. Simple Connections for the Production of Electric Waves. —
Up to this point, have been shown the means by which an oscillating
discharge is produced in a condenser circuit. It is necessary now
to learn how the oscillations can be gotten into an antenna so they
may be sent out as radio waves. The wiring connections for the dif-
ferent methods are given in this and the following sections, showing
first the simplest transmitting connections and then leading up to
standard sets.
The simplest possible wave transmitter is a straight wire cut in
the middle by a small spark gap. See Fig. 191. If the wire were
not cut, and if oscillations could be produced in it, the charges
would travel rapidly back and forth owing to the capacitance and
iuductance of the wire and waves would move out into space as ex-
plained in Chapter 4. The oscillations taking place in the wire are
of the same nature as those in the circuit CL of Fig. 180. The
student should learn to think of the wire as uncut, for the gap be-
comes a conductor when the spark is passing. Oscillations are
produced by the same means described in Section 154, using a high
voltage to start a discharge across the spark gap. This is done by
connecting a transformer or an induction coil to the gap. The use
of an induction coil is shown in Fig. 191. The two halves of the
wire charge up as a condenser until the potential difference rises so
high that the insulating property of the gap is broken down. There
is then a (Jischarge across the gaps and oscillations pass freely until
the energy is spent. The gap then becomes non-conducting again
as has been explained, and permits a renewed charging. The process
is repeated as many times a second as the vibrator works.
The interval from one break at the vibrator to the next may be
about 0.01 second, while it will take only in the neighborhood of
0.00001 second for the discharge to be completely accomplished
266
RADIO COMMUNICATIOX.
(basis of illustration is a wave length of 150 meters, 20 waves to a
train) . Thus it is seen that there is a comparatively large time inter-
val between successive wave trains, in which the gap may cool and be
restored. A sketch of the discharge current is shown in Fig. 192, but
the wave trains are not shown nearly far enough apart for the case of
a, damped oscillator such as that of Fig. 191. To show how relatively
large the time interval between successive wave trains is, it might be
stated that, in this illustration, the length of the wave train itself
compares with the length of the idle interval between wave trains
about in the same ratio as one day compares with three years.
The next theoretical step toward a standard radio transmitting set
is to add large metal plates to the outer ends of the straight wires.
coil)
^
^l|t|l|lh
Fia. H2
Fio. 1^3
Lr\d plated ^r
oscillattn^
Curr*n^
l|i|l|l|H
Looeol See
^
Ip^*
!K
Tlfn«
■V-
ILOI s«c.
U^nrN|»«d WAV* WifNS ( iJot" to scale)
See Fig. 193. This increases the capacitance of the oscillator and
causes larger charges to accummulate for the same potential differ-
ence, thus giving a larger flow of current back and forth in the wire and
sending out more electric and magnetic lines of force. The strength
of signals and the range are thus increased.
It is shown in Section 132 that the lower half of the oscillating
system, Figs. 191 or 193, may be replaced by the ground, the action
of the upper half remaining as before. Also, it is customary to re-
place the upper capacitance plate of Fig. 193 by one or more wires,
RADIO COMMUNICATION,
267
horizouUl or nearly bo. See Fig. 194. A relatively large capaci-
tance can thuB be added, and the confitnictional difficuitiea and
arrangemcnta of support are simplified. This assemblage of wires
forms the "antenna," A variable inductance coil inaerted in the
antenna wire will permit tuning to diHerent frequencies or wave
lei^ths. Thus a simple transmitting outfit is buUt up.
The arrangement shown in Fig. 194 is called the plain antenna
set to distinguish it from the inductively coupled set explained
below. It is a good radiating system, but the waves emitted are of
such high decrement that they cannot be readily tuned out in
receivii^ apparatus when one does not desire to receive them.
See Section 116. Hence this system is not permissible in general
practice, Ita advanU^es besides simplicity are, however, ila
eSectivenesa in cases where the sending operator wants all possible
stations to hear him, aa for instance when a ship needs help, and
secondly its military use in purposely drowning out or "jamming"
other signals which an enemy is trying to receive. The connection
is very quickly made by inserting the spark gap directly between
the antenna and ground wires, and connecting the current source
across the gap. Arcing in the gap must be guarded against, and care
268 RADIO COMMUNICATION.
should be taken not to open the gap too wide, or the antenna insula-
tion may break down.
161. Inductively Coupled Transmittiiig Set. — Instead of connect-
ing the spark gap directly in series with the antenna it may be
placed in a separate oscillating circuit like that of Fig. 180 and this
circuit then coupled with the antenna. In the most common
method the coil of the oscillating circuit (called the "closed " circuit
to distinguish it from the open or antenna circuit) is coupled induc-
tively to the inductance coil in series with the antenna. The cir-
cuits thus become Fig. 195. One of the advantages of this method
is that the condenser in the closed circuit may have much greater
capacitance than the antenna and thus may store more enei^ for
each alternation of the supply voltage; this energy is handed over
to the antenna which thus becomes a more powerful radiator.
Other features of the method are given in Section 163 below.
As ])(ifore, either an induction coil or a transformer with a.c. supply
voltage may be used. In Fig. 195 the latter is shown. Tis an iron
core transformer, somewhat similar in construction to the ordinary
transformer used in electric light systems. The two inductance
coils P and 8 constitute what is sometimes called an ''oscillation
transformer." A hot wire ammeter is in series with the antenna.
The positions of the spark gap and condenser are sometimes inter-
changed , bringing the spar k gap across the transformer. See Fig. 196.
There is no practical difference in the operation.
The condenser discharge cannot take place through the trans-
former T on account of its very great impedance, but passes across
the spark gap and through the few turns of the primary coil P, pro-
ducing a rapidly changing magnetic flux within the coil. The
secondary coil S is placed near or inside of coil P, so that part of the
alternating magnetic fiux of P passes through S. There are three
principal styles of oscillation transformer, the double helix, hinged
coil, and flat spiral types. See Figs. 197, 198, 199. In order to
have a low resistance the conductor is usually a copper ribbon of
large surface, or edgewise wound copper strip. The amount of
coupling, or the mutual inductance, between them is varied by
moving one or both of the pair. Connections are made to such
coils by movable clips, so that any desired amount of self inductance
may be used.
The hot wire ammeter is used for measuring the current in the
antenna circuit. For merely tuning to resonance a low reedstance
RADIO COMMUNICATIOX. 269
lamp such as a email flashlight lamp may be used in place of the
hot wire ammeter, the maximum current being indicated by the
Fro. 197.— Double helix oscillation transrormeri colls sepBrsl«d udally.
1 brightness of the lamp filament. If the current ie too
great for the lamp it should be shunted by a short lei^h of wire.
270 RADIO COMMUXICATION.
The ammeter or lamp may be short cii«uited except when actually
needed, in order t« keep the resistance of the antenna circuit low.
162. Direct Coupled TransmittlnE Set.— Direct instead of induc-
tive coupling may be used between the closed circuit and the
antenna circuit, as is Fig. 200. (Direct coupling wae explained
in Sec. 119). One inductance coil is all that is needed. By the
contacts shown, as much or as little of the inductance as desired
Fig. 198.— Hinged coil osoillstlon Iransformer.
can be used in either circuit. In order to tune to some wave lengths
itmay be necessary to have an additional coil in series in the closed
circuit. By making the part of the inductance that is common to
both circuits a small part of the total inductances in the circuits,
the coupling can be made as loose as desired. Since direct and
inductive coupling are strictly equivalent, the diecuaeion of one
applies to both.
RADIO COMMUKICATION.
271
163. CompatlBoii ol Coupled and Plain Antenna Sets. — In tbe
plain antenna set of F^. 194 the spark gap ia in Heriea with the
antenna. Thus the reaiBtance of the gap is present and helps to
make the decrement of the radiated waves high. While high decre-
ment is an advantage in special
cases, as explained in Section
160, it is usually not desirable.
When the spark gap is in a sep-
aratecircuit, coupled either in-
ductively or directly to the an-
tenna, as in Figs. 195 or 200,
the resistance of the spatk gap
does not enter into theantenna
resistance. The decrement of
the wave sent out by the set
is subject to control The con-
denser in the closed circuit
inaybavelargecapa<.itanceand
thus store a great amount of
energy and, if a plain spark gap is used, produce a dieciiaige that
persists a relati\ ely long time before dying away. This oscillatii^
current in the closed circuit forces oscillations in the antenna of
le small decrement.
When a quenched gap is used, it would make the decrement much
worse if used in the antenna circuit. When used in the closed cir-
cuit, however, the oscillations in the closed circuit have such a high
272 RADIO C0M3IUNICATI0N.
decrement that they stop abnost immediately, and simply start the
antenna circuit oscillating, which thereafter oscillates with its nat-
ural decrement which may be small.
On account of the small decrement of the oscillations in the
antenna circuit the instantaneous voltages do not reach as high
values, with a given current and power output, as they do when
the oscillations are strongly damped. Thus the voltages in the
antenna are not as great, when the coupled circuit is used, and the
antenna insulators are not as likely to fail.
164. Tuning and Resonance. — ^A very pronounced maximum of
current is obtained in the antenna circuit when its natural period of
oscillation is the same as that of the primary circuit. This occurs
when LgC8=LpCp. (See Chapter 3, Section 116). Lg is the induc-
tance of the antenna circuit, including the antenna itself, lead-in
wire and the secondary coil of the air core transformer. C, is the
capacitance of the same circuit. Lp is the inductance of the primary
circuit, and since the wiring is short the inductance is nearly all in
the coil L. Likewise, since C has a large capacitance, Cp is practi-
cally the capacitance of this condenser. It is not necessary in oper-
ation to measure any of these quantities. The hot wire ammeter
will show by trials when the products are equal, or a wavemeter will
enable the operator to adjust each circuit P and S to the same fre-
quency, or to any desired wave length. The principal case where
the inductances and capacitances need to be known is in the design
of a set which differs from previous sets so much that the proper size
of apparatus is not known. To adjust the apparatus to send out long
waves, a large inductance may be used in series with the antenna.
It is preferable, however, to use a large antenna thus obtaining large
capacitance, which stores up large charges and allows a large radi-
ating current.
165. Coupling. — ^When the antenna and closed circuits are adjusted
independently to the same frequency or wave length, and then
closely coupled together, waves of two frequencies appear in each
circuit. See Section 120. For showing the double wave in radio
apparatus, a wavemeter (see Section 112) placed near either of these
coupled radio circuits will be found to indicate a maximum response
at two different wave lengths. If then the coupling between the
two circuits is diminished, the two wave lengths approach each other
and the wave length for which the circuits were set, and at a very
loose coupling only one wave length will be discernible. Figs. 201
RADIO COMMU^^ICATION.
273
to 204 show resonance curves for the case where the primary and
secondary are adjusted separately to 600 meters, and then are coupled
by bringmg the secondary and primary coils near together (when
the coupling is inductive). When the coupling is direct it is made
closer by making a larger part of the inductance of each circuit com-
mon to both circuits. These effects are more pronounced when a
plain or rotary rather than a quenched gap is used.
Fig. 201 might allow of fairly sharp tuning on one of the wave
lengths, but only the energy of one wave could be utilized by a re-
ceiving apparatus. Figs. 202 and 203 would be the equivalent of a
Fiq.20/
l^eftoDAivee cwfva, coi Is sa^rafecT -further R«fter\ane« curv, vry lee«« CM^lifj^
single wave of very broad shape or high decrement, such that the
strength of the signals is nearly the same over a wide range of wave
lengths. In Fig. 204 the signals are strong at, or near, only one wave
length, and diminish rapidly if any of the apparatus adjustments are
changed. This is said to be a "pure '* wave. It is desirable to have
as sharp a resonance ciu've as possible, and hence loose coupling is
the rule when a plain gap is used. The advantage is that all the
power sent out is concentrated into a narrow range of wavelengths,
and that receiving stations can tune to one wave which they desire
to receive at and not receive others.
97340"— 19 18
274 RADIO COMMUNICATION.
Action of the Quenched Gap; Relation to Coupling. — Refer again to
the inductively coupled apparatus of Fig. 195 and to the waves of
Fig. 154 in Chapter 3. Also refer to the description of the quenched
gap in Section 156. The action of the quenched gap is to open the
primary circuit, by suppression of the spark at the end of its first
train of waves (point D in Fig. 154). This prevents the secondary
from inducing oscillations in the primary again, that is, from giving
energy back to the primary. The secondary or antenna oscillations
are not thereafter interfered with by the primary and the antenna
:goes on oscillating until the energy is all dissipated as waves or
Jieat (see Fig. 155). The length of the train will depend only upon
the decrement of the antenna circuit. By reducing the resistance,
the dielectric losses, the brush discharges and leakage, the antenna
current may be made to oscillate for a comparatively long time, at
the frequency for which the set was adjusted . This quenching of the
primary avoids the double waves of Figs. 201, 202 and 203, even with
close coupling. In fact, the coupling should be close for good oper-
ation with the quenched gap. Some cai*e has to be taken in the
adjustment of the coupling, but when adjusted properly this gap
gives a high pitched, clear note. The wavemeter will readily show
when a single sharp wave is obtained (see Section 168), and the sound
in the telephone receiver will indicate the proper adjustment for
good tone. The quenched gap is very efficient, because the close
coupling produces a large current in the antenna.
It is well to note that the principles of operation of the quenched
gap and plain gap are exactly opposite. The former aims to stop
the primary oscillations quickly, after the secondary has been
brought to full activity. The latter aims to keep the primary
oscillations going as long as possible, all the time giving energy to
the secondary as it is radiated away; the coupling is loose and
the primary decrement is kept low. The rapid decrease of the
oscillations in a quenched gap circuit are assisted by having a large
ratio of capacitance to inductance. This has the incidental advan-
tage that the voltages across the condenser and coil are thus kept
low.
166. Damping and Decrement. — If the energy in the antenna cir-
cuit is dissipated at too rapid a rate, owing either to radiated waves
or heat losses, the oscillations die out rapidly and not enough waves
exist in a received train to set up oscillations of a well defined period
in a receiving antenna. Such waves are strongly damped and have
RADIO COMMUNICATION. 275
a large decrement. They produce received currents of about the
same value for a considerable range of wave lengths. Thus selec-
tive tuning is not possible. To increase the number of waves sent
out in each wave train from the open circuit (that is, to make the
oscillations last longer) the resistance of the circuits must be kept
low. When using a plain spark gap the coupling between closed
and antenna circuits must be small enough not to take energy too
fast from the closed oscillating circuits. At each condenser discharge
the primary has a train of oscillations which at best die out long
before another train starts (see Fig. 192); these oscillations are
stopped more quickly, however, if the energy is drawn rapidly out
of the circuit by the antenna. Close coupling is permissible only
when a quenched gap is used, (see remarks at the end of the pre-
ceding section.) With any other kind of gap the secondary is kept
oscillating by energy continually received from the primary.
A great many factors contribute to the resistance of the antenna
circuit, and this must be kept as low as possible. The antenna
must have a good, low resistance ground, must use wires of fairly
low resistance, and must not be directly over trees or other poor
dielectrics. The resistance of the closed circuit particularly must
be very low. Heavier currents flow here than in the antenna wires.
For this reason the closed circuit wires should be short and of large
siuiace, preferably stranded wires or copper tubing. The condenser
should be a good one, free from power loss.
167. Additional Appliances. — ^A number of additional appliances
are necessary or desirable for the operation of a damped wave gener-
ating set. The operation is improved by having a variable reactance
(iron core inductor) in series with the alternator, to tune the alter-
nator circuit to the alternator frequency. See C. 74, p. 230.
Changes of Wave Length. — In many sets of apparatus it is cus-
tomary to have connections arranged by means of which different
chosen wave lengths, say 300 or 600 meters, can be transmitted with-
out the necessity of a readjustment of the apparatus after each
change. An antenna alone without any inductance coil has a natural
wave length of its own, dependent upon its inductance and capaci-
tance. See Sections 116 and 145. The antenna is usually so designed
that its natural wave length is shorter than the wave length to be
used, and the wave length is brought up by adding inductance in
series or merely by the added inductance of the secondary of the
oscillation transformer. In the case of a small antenna such as
276
RADIO COMMUNICATION.
that on a small ship, it is necessary to use a large inductance. Since
it is desirable to have the coupling loose, a part of the secondary
inductance can be in a separate coil called the antenna ''loading
coil.*' This is coupled to the primary. Fig. 205 shows this arrange-
ment. For a quick change of wave length a single switch is often
provided, which, by a mechanism of levers, changes simultaneously
the adjustments on all three coils. From these coils are taken out
taps over which three switch blades pass adjusting all the induc-
tances to approximately the values needed for the particular wave
length desired, keeping the circuits in resonance and at the proper
coupling. For fine adjustments an additional variable inductor
may be provided in the primary and in the secondary.
Fig. 205 also shows an arrangement whereby the operator can ob-
tain wave lengths shorter than the natural wave length of the antenna
^
Fiq. Z05
cott
BP^^=^^
-
ck;?
Tnairy* mitt i i\fe S«t , ^Ko w i f>^
Fia. ZOh
\\l
Connection df'+our
con<i«n5«n«
by inserting a condenser in series, (see Section 35), in the antenna
circuit. In this case the loading coil will be set at zero turns to di-
minish the wave length. The condenser inserted must be capable
of withstanding high voltages similar to those in the main trans-
mitting condenser. By using a small capacitance the wave length
can be reduced to approach one-half of the natural wave length.
It should not be reduced that much, however, for the radiation is
inefficient if the condenser is too small. A zero capacitance (an
open circuit cutting off the antenna entirely from the ground)
would be necessary to produce half wave length exactly.
Clidke coils. — Fig. 205 shows also choke coils to prevent the high
frequency condenser discharge from getting into the transformer
and puncturing the insulation. The coils choke down the radio fre-
quency current but do not obstruct the low frequency chaiging
RADIO COMMUNICATION. 277
current from the transformer. They must be specially designed so
that they do not have capacitance enough to allow the radio fre-
quency current to pass. They can often be dispensed with.
168. Adjustment of a Typical Set for Sharp Wave and Radiation. —
The set is assumed to be an inductively coupled set, arranged as
in Fig. 205. The first step in adjusting it to work properly is to tune
the closed circuit to the wave length which is to be used. This is
done by the aid of a wavemeter having in its circuit a sensitive hot
wire ammeter. The wavemeter is placed at a distance of one or
more meters from the coil of the closed circuit, and with the set in
operation but the antenna circuit opened, the wavemeter coil is so
turned that a small current is observed in the wavemeter ammeter.
With the wavemeter set at the chosen wave length the closed cir-
cuit inductance is varied until resonance is obtained. If no reso-
nance point is found it is probable that the closed circuit inductance
or capacitance is either too large or too small. This inductance
should be varied and a resonance point will be located after a few
trials.
The next process is to adjust the coupling to obtain a piu^e, sharp
wave, that is, to get as much of the power as possible into the wave
length that is to be used. With both antenna and closed circuits
closed, the coupling between them is varied. If the spark gap is not
a quenched gap, the coupling is first made fairly loose and the antenna
loading coil is varied until resonance is obtained, as observed on the
hot wire ammeter in series with the antenna. The coupling is then
made closer imtil two points of resonance appear. It is desirable
to have a piu^e wave, that is, have only one resonance point. There-
fore the coupling is loosened until it is certain that there is just one
sharp point of resonance. If the set has a quenched gap, the coup-
ling is kept close, and varied only enough to insiu^e a single, sharp
wave.
It is necessary next to adjust the apparatus to give maximum
current. Keeping the wave length and coupling adjustments
fixed, vary the voltage and lengtn of the spark gap and the induc-
tance in series with the alternator until a good clear spark tone and
maximum current in the antenna circuit are obtained. It is desir-
able to repeat the coupling adjustment and then this adjustment
again. When the set has a quenched gap, best operation is usually
obtained when the inductance in series with the alternator (Sectior
167) is somewhat greater than that required for resonance to the
alternator frequency.
278 RADIO COMMUNICATIOX.
169. Efficiency of the Set. — To maintain good efficiency, all resist-
ances in the circuits must te kept as low as possible. A number of
suggestions for keeping resistances low were given in Section 166.
It is also necessary to avoid brush discharges and arcs, to keep all
connections tight, condenser plates and other parts of circuits free
from dust and moisture, and antenna well insulated. Brush dis-
charges may be reduced by eliminating sharp points or edges on
conductors, or by coating the edges of metal plates with paraffin.
The guy wires of the antenna should be divided into short lengths
with insulators between them, to reduce the flow of current in them.
The inductance coils and the spark gap must be properly designed.
The efficiency may be defined aa the ratio of the power radiated
away as electric waves from the antenna to the power input in the
transformer. The power input P in the transformer may be meas-
ured by an ordinary wattmeter. The power radiated from the
antenna can be expressed in the form RP where / is the current
in the ammeter at the base of the antenna and R is the radiation
resistance. The efficiency is then RP divided by P. As explained
in Section 143, the radiation resistance cannot be measiu-ed directly,
but can be found from the total effective antenna resistance by
subtracting those resistances which give rise to heat losses.
Representative values for the efficiency of the entire set are 2
per cent to 15 per cent. The transformer efficiency may be roughly
85 per cent to 95 per cent. The closed oscillation circuit losses are
very large in proportion to the power transferred, a fair value of
efficiency being about 25 per cent (by careful design and adjust-
ment using the quenched gap this may sometimes be increased to
50 per cent). The efficiency of the antenna circuit (radiated power
divided by power given to the antenna) may be between 20 per
cent and 2 per cent or lower, or may be made as high as 50 per cent if
special pains are taken. The product of the three separate percent-
ages gives the over all efficiency. For an interesting table of com-
parative values of efficiencies, see J. A. Fleming's ** Wireless Teleg-
raphist's Pocket Book," pp. 221 and 223.
170. Calculations Required in Design.— This section gives methods for determin-
ing the values of condensers and coils to be used in transmitting apparatus, and
enables one to calculate the capacitance or inductance of such condensers and coils
as are commonly employed. The most important design formula is the one for
wave length,
Xm=1884.VC'i
where Cis in microfarads and L in microhenries and a in meters.
RADIO COMMUX ICATIOX,
deoser cbarg«3 per aecondj and £^ is tl
from this that H a low voltogB £> Is use
will be Urge and If a lii:;1i Tollag? is use<
a, large reduction of caTBritance with a ;
lerm is squarad, tberetore to avoi-i usi
ktta, if is tlie numbei of con-
it. in volts. It may be soon
ice neeilod for a given power
■e may be smaller. Thero b
1 volta^ because tbe voita:^
Fi "*"
(
He
.,
<
1
2o
Fia. ZIO
r,a-lM
2^-3'.
i
t£J*"'
3id..™«ffl-T,f-U
as high a voltage as poAstble without brush discharge taking place. For instance,
i( the voltaje were doubled, a condenser only one fourth as large could be used tw
tho same power. As an illustration, If it is desired to use ) kw. at 12,000 volts, with
1000 sparks per second,
C-O.C18S5Xja Xfi"^
280
RADIO COMMUNICATION.
where JTis the dielectric constants n is the number of sheets of dielectric^ 8 is the area
in cm.s and r the thickness in cm. Supposing that mica is not available, it may be
required to find the number of sheets of glass required to make up the condenser
of 0.007 mfd. required above. Suppose the sheets are 15 by 20 cm., 0.25 cm. thick,
and the dielectric constant is 7. Substituting in the formula just given,
»■
0.25X0.007X 10'
"0.0885X7X15X20
=-9
Thus nine sheets of this dielectric are needed.
It should be noted that the higher the spark frequency N, the smaller may be the
condenser used to give the same power. For this reason, as well as the others previ-
ously given, it is a distinct advantage to use a high spark frequency.
When the voltage at which it is desired to operate the spark gap is so high that it
will break down the particular insulation used in the condensers, or cause brush
discharge, the connection of four condensers each of capacitance C, as shown in Fig.
206, p. 276, will give a resultant capacitance C, while subjecting &^h condenser to
only half the full voltage.
Inductance Coils. — The principal inductance coils in a radio set are the primary
and secondary of the oscillation transformer and the antenna loading coil, and the
. ria. zii
3o:oD
Fi<3. 212
0»5» faction •f Mi»IWi)fcr c«il
I
Flo. 213
o:o:oioioiao:o:o
Cr0SA ^•eti'«naf<ir^l« Uy«rc«f
three corresponding coils of the receiving set. The three coils, oscillation primary,
and secondary, and loading coil, are very similar. In actual practice few operators
know even approximate values of the inductances; a standard form is used, depend-
ing somewhat on the size of the set, and adjustments by clips or taps enable the
proper values to be used. In order to design a set, the inductances of the coils are
calculated and an allowance made for the small inductance in the leads and other
parts of the circuit. Tlie form usually used for coils in transmitting circuits are
either the helix (sinjlo layer spaced coil) of round wire, or edgewise wound strip.
Figs. 207 and 208, or the flat spiral or pancake of bare metal ribbon. Figs. 209 and
210. For wavemeters a multi-layer coil is used having wires insulated and close
together, Fijs. 211 and 212. For receiving coils the common form is a single layer
of insulated wires, Fig. 213. The coil s are supported or held together by some insulat-
ing material, and no iron is used in them.
RADIO COMMUNICATION.
281
HelU of Round Wire.~The inductance of the coil of Fig. 205 is given in micro-
henries by
, 0.0395a«n«Jr
L V (89)
where a and b are shown in Fig. 211, a being the tnean radius qi the solenoid and b
the total length of the solenoid; n is the number of turns of wire; d is the diameter
of the bare wire; and JTis a shape factor depending upon the relative dimensions,
all lengths being expressed in centimeters. A brief table of values of K is given
below. In the figure, D is the pitch of the winding or the distance between centers
of adjacent wires; c is the radial thickness of the winding.
As an example, find the inductance of a solenoid having 15 turns of bare wire of
diameter 0.4 cm., pitch of winding 1.1 cm., diameter of core 24 cm. In the formula
d— 0.4 cm., D— 1.1 cm., n=15, 6=-nD— 16.5 cm., a= 12+. 2= 12.2 cm. Then with
-^— r^ — 1 .48, K is found as 0.598. From the above formula the inductance in micro-
16.
henries is given by
i-
0.0 395X12.2«X 15a
16.5
X 0.598-= 48.0
II it is desired to compute the inductance more closely than a few per cent, more
accurate formulae should be used as given in C. 74, p. 253.
TABLE OF VALUES OF K.
(Shape Factor of Helical Inductance Colls.)
Diameter
K
Diameter
K
Diameter
K
Length
Length
Length
0.00
.C5
.10
.15
.20
.25
.30
.CO
• \J\J
.00
1.000
0.979
.959
.939
.920
.902
.884
.850
.818
.789
0.70
0.80
O.GO
1.00
1.25
1.50
1.75
2.00
2.50
3.00
0.761
.735
.711
.688
.638
.595
.558
.526
.472
.429
3.50
4.00
5.0
6.0
7.0
8.0
9.0
10.0
25.0
100.0
0.394
.365
.320
.285
.258
.237
.219
.203
.105
.035
Helix of Edgewise Wound Strip. — Hefer to Fig. 208. For this case the formula is
0. 0395 osnaz 0. 0126 rUac
i=
(90)
b b
microhenries, where K is given in the table above.
As an illustration of use of the formula, a helix of 30 turns is wound with metal
strip 0.635 cm. wide by 0.159 cm. thick with a winding pitch of 0.635 cm., to form a
solenoid of mean diameter 25.4 cm. Here D^O.635 cm., a=12.7 cm., c»0.635 cm.,
2fl
6= ?ii>= 30X0.635= 19.05 cm. For -5—1.333, £"=0.623.
Then from the above formula
^ 0.0395X12.78X900X0.623 0.0126X900X12.7X0.635
19.05
X=. 187. 4-4.0
X— 182.5 microhenries.
19.05
282
RADIO COMMUNICATION.
Flat 8pirai,See Figs. 209 and 210. The inductance is given by
i-0.01257 amx [2.303(l+3^+^)logi« ^-^i+i^, Vz]
(91)
where a— ai+i (n-l)D; d— -Jb^+c^; and yi and yz are shajpe factors civen in the follow-
ing table. See example below.
Shape Factors for Flat Spiral Inductance.
b/c
yi
ys
' b/c
1
yi
ys
asoo
a 597
a 50
0.796
a 677
0.025
.525
.598
.55
.808
.6C0
.05
.549
.599
.CO
.818
.702
.10
.592
.602
.65
.826
.715
.15
.631
.608
.70
.833
.729
.20
.665
.615
.75
.838
.742
.25
.695
.624
.80
.842
.7^:6
.CO
.722
.633
.85
.845
.771
.35
.745
.643
.90
.847
.7C6
.40
.704
.654
.95
.848
.8C1
.45
.782
.665
1.00
.848
.816
Illustration.— A flat spiral of 38 turns is wound with copper ribbon whose cross
sectional dimensions are 0.953 cm. (3/8 in.) by 0.795 cm. (1/32 in.), the inner diameter
being 10.3 cm., and the measured pitch 0.4 cm. Here n«38, 6—0.963, D— 0.4, cnD^
37 ,
38X0.4-= 15.2 cm.; 2ai=10.3 therefore a-5.15+ 2X0.4-12.55 cm.; i- V0.fl53'+15.2»—
15.23 cm.; -J -6.592; 322^-0.0002; ^,-0.0152; j^ -0.091 ; 6/C-0.0627. Then from
the table, yi— 0.5604 and ys— 0.599. From the above formula,
i-O.O1257X12.55X38«Xl2.3O3Xl.O15Xlogio6.592-O.56O4+O.O01XO.5991
Zr— 323.3 microhenries.
This is correct to § of 1 per cent.
Multi-Lay er Coil. — The coil is made of insulated wire closely wound as in Fig. 211.
Sudi coils are used in wavemeters. The insulating frame on which the coil is wound
has the cross section shown in Fig. 212. The inductance is given by
^_0.0395^a.n.ir_0.0126«^ ^^^^^
where Eis given by the following table:
b/c
E
b/c
E
1
0.000
12
0.289
2
.120
14
.296
3
.175
16
.302
4
.208
18
.306
5
.229
20
.310
6
.245
22
.313
7
.256
24
.316
8
.266
26
.318
9
.273
28
.320
10
.279
30
.322
RADIO COMMUNICATION.
283
As an illustration, a coil has 15 layers of insulated wire, with 15 turns to a layer
the mean radius being 5 cm. The coil is 1.5 cm. deep and 1.5 cm. in axial length.
Here a=5, n=>225, 6=c=1.5. From the tables K is 0.267 and E is zero. Then the
formula gives
l.D l.d
i= 8887-2205
I,= 6682 microhenries.
Single Layer CoiZ.— Refer to Fig. 213. The inductance is computed by the formula
(89). As an illustration, a coil has 400 turns o! wire in a single layer, pitch of winding
0.1 cm., radius of coil out to center of wire 10 cm. Here a== 10, n=400, D=0.1, 6=nD
-40. With $=?^=-0.5, K is found as 0.818.
40
i=
0.03948X100X4008
40
X 0.818= 1290 microhenries.
For any other inductance calculations see C. 74, Sections 66 to 73.
171. Simple Field Measurements. — On high power radio trans-
mitting sets it is desirable to have instruments reading the current
taken from the generator, the voltage of the same, the power so
taken and the frequency of the current. The four instruments,
ammeter, voltmeter, wattmeter and frequency meter, are perma-
nently mounted on the switchboard. The measurements of the
various radio quantities are explained below.
Voltage. — ^A simple method of measuring a voltage, either at radio
or low frequencies is to measure the distance a spark jumps between
electrodes of a given shape and size in air. Following is a table
showing approximately the ''spark voltages" in air between brass
balls 2 cm. in diameter for various spark lengths.
Spark
Length in
Spark Voltage.
Cm.
0.1
4,700
0.2
8,100
0.3
11,400
0.4
14, £00
0.5
17, £00
0.0
20,400
1.0
31,300
2.0
47,400
Current. — ^The principal current measurement in practice is that
of the current in the antenna. A hot wire ammeter is inserted in the
lead-in or ground wire. If its reading is lower than normal, it indi-
cates trouble in the adjustment of the apparatus, or in the grounding.
284 RADIO COMMUNICATION.
and means decreased distance of transmission. In order to avoid
undue interference with other stations, the ammeter current should
be kept as small as will give the needed range. As has been stated
before, a low resistance lamp can be used in place of the ammeter.
When the closed circuit and antenna are not in resonance, the lamp
biums feebly or not at all. Current measurements are also necessary
in connection with some of the various measurements.
Wave Lengths. — ^The theory and use of the wavemeter have been
discussed in Sections 112 and 168. A wavemeter placed in inductive
coupling with a coil or antenna carrying radio current will show pro-
nounced increase of current in its own coil and condenser when it is
tuned to resonance with the source. The wave length is read
directly from the wavemeter setting for resonance, or from a calibra-
tion curve. A receiving set can be used to measure the wave lengths
of received waves if it is first standardized in terms of wave lengths.
This standardization is done by the arrangement of apparatus shown
in Fig. 214, where Z is a buzzer, LC & wavemeter, and A the induc-
tance coil of the receiving circuit.
The operator listens in the telephone of the receiving set, (not
shown in the figure). As the wavemeter condenser knob is turned
the loudest sound is heard when the wavemeter circuit is tuned to
the same wave length as that for which the receiving set is adjusted.
The wave length is then read from the wavemeter scale or calibration
curve. Continuing in this manner, the receiving circuit can be
calibrated as a wavemeter, by setting it at many different adjust-
ments and reading the wave lengths at resonance each time. The
wavemeter need never be used, after that, for received waves, and
the operator always knows where to tune for any wave length.
Inductance. — ^To find the unknown inductance Lx of a coil, a
tuned source, which need not be a wavemeter, is excited by a buzzer,
shown at Z in Fig. 215-A. A wavemeter with a coil of known induc-
tance L is brought near and its variable condenser C adjusted to
resonance by means of a detector and telephone. L is then replaced
by Lx and a new value of capacitance Ci is found for resonance.
C /X \*
Then L C=Lx Ci and Lx is found as L ^r, or as L ( r- j if the waveme-
ter reads directly in wave lengths. The value thus measured is the
apparent inductance which depends somewhat on the frequency of
oscillation. (See Section 114.) Values of Lx can be obtained at
different frequencies of the source.
izri^ —
^ 1
o
b
^5
"C
o
H
^ 1
L<=^
" S
*-o
i
o
^
§/f
Tiq. 214
Wavt Lengrh Ca//if ration
of a R9ctivm<j Set
r©-^
Ti(}. ZI5-A
vQH^-
^.
Fif Zl5-d
Ti^. ZIb-A
rdH'l'
C. L
lb
II
I
Ti(j. ZI6-B
■^
■VWWV '
F/f zn
285
286 RADIO COMMUNICATION.
A second way is by the use of a standard condenser instead of a
standard coil; (See Fig. 215-B). Lx is connected to the standard
condenser C and that circuit is set in oscillation by the buzzer Z,
The wave length is measured by a wavemeter, and L^ is computed
from X^= 1884 V&A^
Capacitance of condensers, — The simplest method is that of com-
parison with a standard variable condenser. A tuned circuit LC
is excited by a buzzer, Z in Fig. 216-A. The unknown condenser Cp
is placed in series with an inductance coil X, and the buzzer circuit
adjusted to resonance, using the detector and telephone of the
circuit under test. The unknown condenser Cx is then replaced by
the standard condenser Cg which is now adjusted to resonance with
the buzzer circuit. The capacitance of the imknown condenser
is then the same as that read on the standard.
If a standard condenser is not obtainable, the capacitance of the
unknown variable condenser can be found by connecting it to an
inductance of known value L and exciting the circuit by a buzzer.
The wave length is read on a wavemeter (Fig. 216-B). Cx is found
from XTO = 1884V^r.
Accurate results are easily obtained by the first method described,
that of comparison; but the second method is open to error because
of the distributed capacitance of the lead wires and the coil, and
the inductance of the leads. The effect is slight if the capacitances
employed are large.
Resistance and Decrement. — Three simple methods are available
for measurement of high frequency resistance or decrement, (1) resist-
ance substitution, (2) resistance variation, and (3) reactance varia-
tion. After the resistance R is known, a simple relation 5=19.7 R/C
enables the decrement to be computed, or vice versa. C is the
capacitance at resonance and is known from the condenser setting.
Of the three methods, the first is the best if a variable high frequency
resistance standard is available; the second is a good all round
method, requiring resistance standards, but these need not be varia-
ble; the third requires no resistance standard, and is especially
suited to measuring the decrement of a wave. In all three methods,
the best results are obtained if the exciting source gives continuous
or only slightly damped current. In the resistance substitution
method, the resistance R to be measured is inserted in a timed
circuit with a variable condenser C and inductance coil L coupled
loosely to the source, as shown in Fig. 217. A hot wire ammeter is
RADIO COMMUNICATION. 287
inserted at A. The circuit is tuned to the source and the reading
of A noted. The resistance R is then replaced by a variable resist-
ance standard which is adjusted until the ammeter reading is the
same as it was before. The known amount of resistance inserted
is the same as R, Resistance standards for radio work must be of
fine wire to avoid skin effect, and must be short and straight in order
to have very little inductance. For additional information on
measurements see Circular 74.
B. Apparatus for Undamped Wave Transmission.
172. Advantages of Undamped Oscillations. — ^Undamped oscilla-
tions are not broken up into groups like damped oscillations.
Exactly similar current cycles follow one another continuously,
except as they are interrupted by the sending key, or subjected to
gradual fluctuations of intensity as when used for radio telephony.
Undamped oscillations are produced by a high frequency alternator,
an arc, or vacuum tubes. This chapter does not take up vacuum
tubes and their uses, these being treated in the following chap-
ter. The main advantages of undamped waves are the following:
(1) Radio telephony is made possible. (2) Extremely sharp tuning
is obtained and consequent reduction of interference between sta-
tions working close together. A slight change of adjustment throws
a receiving set out of tune, and the operator may pass over the cor-
rect tuning point by too rapid a movement of the adjusting knobs.
(3) Since the oscillations go on continuously instead of only a small
fraction of the time, as in the case of damped waves, (Section 160)
their amplitudes need not be so great, and hence the voltages
applied to the transmitting condenser and antenna are much lower.
(4) With damped waves the pitch or tone of received signals de-
pends wholly upon the number of sparks per second at the trans-
mitter. With undamped waves the receiving operator controls the
tone of the received signals, and this can be varied and made as
high as desired to distinguish it from strays, and to suit the sensi-
tiveness of the ear and the telephone. These advantages, freedom
from interference from other stations through selective tuning, the
use of high tones and low voltages, and the greater freedom from
strays combine to permit a higher speed of telegraphy than could
otherwise be obtained.
173. Use of High Frequency Alternators. — For the production of
continuous oscillations an alternating current generator of very high
288
RADIO COMMUNICATION.
frequency can be used. See Section 95. This is connected directly
or inductively to the antenna and ground. See Fig. 218. This
constitutes the simplest possible connection for producing continu-
ous waves. However, to obtain a wave length as short as 1500
meters, the frequency of the alternating current must be as high as
200,000 cycles per second. The generator speed requfred to pro-
duce this frequency is so high that a special type of construction is
needed for such a machine. It is also necessary to have apparatus
for keeping the speed constant, so that the wave length will not
change (since /X„j=300, 000, 000). This method is not available for
Fid. Z\d
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Are a€t "{or |»no«lwetior\ of
generating very short waves; for these, the oscillating vacuum tube
is used. See Section 198.
174. Arc Sets. — ^A much used method for producing undamped
waves of rather great wave length is by means of a d.c. arc operated
on about 500 volts. It has been discovered that an electric arc
between proper electrodes shunted by an inductance coil and a
condenser will produce undamped oscillations through the shunt
cfrcuit. The connection is shown in Fig. 219. The operation is as
follows.
RADIO COMMUNICATION. 289
The current through the arc is always in the same direction but
may vary in magnitude. It is found that when the ciurent in the
arc increases, the voltage at its terminals falls off (see Fig. 220).
Suppose the arc to be burning steadily with the CL circuit discon-
nected. If now the circuit is connected, the condenser C b^ns
charging with the left plate in Fig. 219 positive, and draws current
away from the arc. The potential difference of the arc increases
(Fig. 220) and helps the charging. The charging continues until
the counter emf. of the condenser equals that applied. As the
charging nears its end, the charging current becomes gradually less,
and the arc current as a whole increases to its normal value, with a
corresponding drop in voltage. The condenser then begins to dis-
charge downward through the arc, increasing the arc current, and
lowering its voltage. Lowering the voltage across the terminals of
the arc aids the condenser to discharge, and the effect of the induc-
tance in the circuit tends to keep the current flowing, and a charge
is acciunulated on the condenser plates of the opposite sign from the
first one. As the charge now nears its end, the charging current
downward through the arc becomes gradually less, and the arc
current decreases, causing the voltage to rise. From Fig. 219 it is
seen that the rise of d.c. voltage is such as to attempt to charge the
left plate of C positive, and the positive charges on the right hand
plate begin at once to come back, going up through the arc and
decreasing the ciurent. There is a consequent further rise of vol-
tage (Fig. 220), and in a direction to assist first the condenser di&-
charge, and then the recharge in the opposite direction (on the left
hand plate). The action now begins all over again, and thus con-
tinuous oscillations take place through the circuit.
Use is made of this phenomenon by coupling the coil L to the
antenna, as in Fig. 221, where the schematic diagram of a complete
arc transmitting set is shown. The d.c. generator is shown with
choke coils KK to prevent the high frequency oscillations from get-
ting back into the generator. 5 is a ballast resistance. A larger oscil-
lating ciurent is produced if the arc is burned in a strong magnetic
field, producing a quenching action on the arc, and for that purpose
the magnets Jl/Jf are provided. Also the arc bums in a closed cham-
ber having hydrogen passing through. The positive electrode is
copper and the negative solid carbon, both being of large size and
cooled by a water jacket. The shunt circuit CL is the same as in
Fig. 219. The key is arranged to short circuit some of the turns of
97340*'— 19 19
i
290 RADIO COMMUNICATION.
inductance in the antenna circuit, the correct number of turns
being adjusted for resonance with the key closed. Then with the
key open, the antenna circuit is out of tune with the arc oscillations
and the ciurent is negligible, thus forming the intervals between
dots and dashes.
A simple modification of Fig. 218 or Fig. 221 will enable the appa-
ratus to be used for radio telephone transmission. One method is
to insert in the ground wire a telephone transmitter capable of carry-
:ing the antenna ciurent. The vibrations within the transmitter
wcaused by soimd waves alter the resistance and modify the radio
.oscillations and transmitted waves. ^
175. Calibration and Adjustment of Sets. — ^With a high frequency
^alternator the frequency and hence the wave length are determined
by the speed of the generator and the number of poles. The induc-
tance and capacitance of the antenna should be of such values as to
give the circuit the same natural frequency as the generated current.
This is brought about by adjusting the antenna loading coil to give
maximmn current in the hot wire ammeter (Fig. 218).
Much the same method is used with arc sets. The desired wave
length is obtained by adjustment of C or Z in Figs. 219 and 221, the
antenna circuit being opened, and the wave length being set on a
wavemeter which is brought near. The antenna circuit is then
adjusted to the same wave length by varying the loading coil until
the hot wire ammeter gives a maximmn reading. A pilot lamp can
be used instead of the ammeter, since it can be adjusted by a shunt
to light only when the circuits are in resonance. Sometimes this
lamp is connected inductively by a loop of wire instead of being
directly in the ground wire.
C. Apparatus for Reception of Waves.
176. General Principles. — Receiving sets are divided into two
general classes, those for damped waves, and those for undamped
waves. Sets for damped waves in practice involve the simpler con-
nections and form a good starting point for the discussion, although
it will be shown later in introducing undamped wave sets, that a
iln Chapter 6, Sections 202 to 204 this action is explained, and improved methods
are given for carrying on radio telephony by means of vacuum tubes. For discus-
sion of the behavior of an electric arc, and its application to radio work, the reader
is referred to Fleming's Principles of Electric Wave Telegraphy and Telephony
(3rd edition), pp. 95 to 115, with special notice of pp. Ill and 112.
RADIO COMMUNICATION.
291
very slight modification of the damped wave apparatus will give
one method of receiving undamped waves. Damped waves are
commonly received by a crystal detector or a vacuum tube detector
(see Sections 179 and 191) and a telephone receiver. The tone
heard in the telephone is that of the groups of damped waves.
Undamped waves are ordinarily received by a vacuum tube method
which produces beats (see autodyne method, p. 336). These will be
made clear in the diagrams which follow, where, for the purpose of
explaining principles, the simplest possible sets will be shown first,
even though not now used in military work.
The fundamental principle of reception of signals is that of reso-
nance. If the receiving circuits are tuned to oscillate at the same
V FiQ. lU
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Fia. 225
2im^l« tuned
receiving
I
natural frequency as the incoming waves, then these waves, though
extremely feeble, will after a few impulses, build up comparatively
big oscillations in the circuits. In reality, then, for reception of
signals, all that is needed is an antenna circuit tuned to the same
wave lengths as that of the transmitting station, and an instrument
capable of evidencing the current which flows in the antenna con-
necting wire. This is shown in Fig. 222. This is the simplest pos-
292 RADIO COMMirXICATION.
sible arntngement for reception, and will operate on either damped
or undamped waves. A current indicating instrument is shown at A .
In practice the current is too feeble for any hot wire anmieter. An
ammeter is more suitable for quantitive measurements than for
receiving tel^raphic signals, since the dots and dashes are not
readily distinguished unless made so slowly as to be impracticable
for transmitting messages.
Use of the Telephone. — A more sensitive receiving device is a tele-
phone receiver having a large number of turns of wire compactly
wound. The current is made inanifest by vibrations of the dia-
phragm at audible frequency, but the frequency of a radio current
is so high that the diaphragm cannot possibly follow it. The effect
is as if the diaphragm tried to go both ways at once, with the result
that no observable motion takes place. To remove this difficulty a
crystal rectifier is put into the circuit, which permits current to
flow in one direction, but not in the other; or more exactly, the cur-
rent in the reverse direction is negligibly small compared with the
current in the principal direction. See Fig. 51. Referring to the
reception of damped waves, it is well to remember that the waves are
in widely separated groups. The action of a cystal rectifier upon
damped oscillations is shown in Fig. 223; the lower halves of the
waves are drawn dotted to indicate the portion of the current that
is cut off by the rectifier.
It is found that the cumulative effect of one group or train of waves,
for instance that due to one condenser discharge at the transmitter,
pulls the telephone diaphragm away from its neutral position.
The number of such pulls per second is equal to the number of wave
trains per second. With a 300-meter wave having 1000 wave trains
per second the radio frequency is 1,000,000 and the audio frequency
is 1000, or one is a thousand times as high as the other. The upper
limit of audio frequency for the human ear is 16,000 to 20,000 sound
waves per second, so that even if the telephone diaphragm could,
without a rectifier, follow the radio frequency, the ear would not
hear the signals. In telegraphic signaling, either a dot or a dash
lasts long enough to contain many wave groups, and in the telephone,
where the pitch corresponds to the spark frequency, a tone is heard
during the length of the dot or dash.
Simple Receiving Sets. — In Fig. 224 is shown the simplest con-
nection for reception with a telephone receiver. It is suitable
only for damped waves. At D is shown the rectifier, commonly
RADIO COMMUNICATION. 293
called a "detector," although it detects nothing; it alters the waves
so that the telephone can detect them. The apparatus as shown
receives best from a transmitter of the same, or nearly the same
wave length. It is true that the presence of the detector and tele-
phone introduces high resistance in the antenna circuit and thus
renders it not very selective, so that it will respond to a wide range
of wave lengths. Tuning to resonance is made possible if a tuning
coil is introduced such as L in Fig. 225, to vary the inductance of
the circuit and hence the wave length. This is a connection exactly
analogous to the plain antenna of Fig. 194, with the spark gap (the
point where the energy enters the antenna) replaced by the detector
and telephone (the point where the used energy leaves the antenna).
It is well to notice how simple is the apparatus actually needed
for reception, contrary to what the uninitiated person supposes.
Three pieces of apparatus, telephone receiver, rectifier and tuning
coil will receive effectively from damped wave stations. The
main disadvantage of the connection of Fig. 225 is in not being able to
tune out stations that one does not wish to hear. Also the ampli-
tude of the oscillations is much diminished by the high resistance
of the detector and telephone. The principal resistance is that
of the detector.
The apparatus of Fig. 225 gives about the same results if the
telephone is in shunt with the detector instead of in series with
it. In this case the explanation of the action is as follows. Sup-
pose that the current flows easily upward through the rectifier, but
not downward. During a group of incoming waves, the antenna
thus receives an accumulated positive charge, and during the
intervals between wave groups it discharges downward through the
telephone. It cannot send current downward through the rectifier.
Thius pulsations of current pass through the telephone with suc-
cessive wave groups.
177. Typical Circuits for Beception of Damped Waves. — To avoid
the difficulties attendant upon the presence of the detector in the
antenna circuit, it is customary to place the detector in a separate
circuit coupled to the antenna; or another viewpoint is that the
detecting instruments are placed as a shunt to the tuning coil.
For instance Fig. 226 is an improvement and requires no more
apparatus than Fig. 225 except that the tuning coil has two adjust-
able connections instead of one. Oscillations now take place
freely between the antenna and ground. Two telephone receivers
are diown, connected in series, one for each ear.
294
RADIO COMMUNICATION.
Direct Coupled Receiving Set. — A further improvement, as regards
selectivity, is shown in Fig. 227, where a variable condenser Cj haa
been added. This is called the direct coupled connection. Let
Li be the inductance in the antenna circuit, Ci the capacitance
between the antenna and ground, and Lj and C2 the corresponding
constants of the closed circuit, shown by heavy lines. The antenna
circuit is called the primary, since the energy enters the set there.
The circuit containing L2 and C2 is called the secondary and is
the closed oscillating circuit. In the same manner in which the
transmitting antenna circuit is a good radiator of power, so the
receiving antenna circuit is a good absorber. It is tuned to reso-
nance with the incoming waves by adjustment of ip The power
ia given over magnetically to the secondary, which is tuned to
V
Fia. 226
V
receivif)^ s^
Fia. 2Z1
O
T^ Direct coupled rae«ivink Sftt
resonance by adjustments of Xj and Cg. Comparatively large
oscillations result in the secondary, producing voltages across the
condenser which are detected by the crystal and telephone, and
which are not in either oscillating circuit. The oscillations are
not damped thereby, and sharp tuning is obtained.
Attention is invited to the analogy of Fig. 227 with the coupled
transmitting set of Fig. 200 in Section 166. The open absorber of
one corresponds to the open radiator of the other; the closed oscil-
lating circuits correspond, each having its L and C; shunted around
the condenser in one case (Fig. 227) is the apparatus where the used
energy is taken out, namely, the detector and telephone, and in
the other case the apparatus where the energy is put in, namely, the
power transformer with its generator.
RADIO COMMUNICATION.
295
Indvjctiveby Coupled Receiving Set, — In Fig. 228 is shown the in-
ductively coupled receiving set. This may be taken as the standard
upon which all later changes are based. A fixed condenser of about
0.005 mfd. is shunted around the telephone and this increases the
strength of the signals. Its action is explained as follows. Suppose
the principal current flows downward through the detector and
telephone. While this current flows, the fixed condenser is charged
with top plate positive. When the reversal of the radio oscillation
comes, the current through D and T ceases. Then the condenser
discharges down through T and tends to maintain the current till
the next oscillation downward through the instruments. In this
V
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FtQ. 221
t
R«c«iivin^ ci'rcwi'ta -fwr v«ry
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way the gaps between the successive pulsations of rectified current
are filled in, and the cumulative effect of a wave group is strength-
ened. In practice the telephone cord, containing as it does two con-
ductors separated by dielectric, forms a condenser which in some
cases is sufficient so that an added fixed condenser gives no improve-
ment.
The connection in Fig. 228 is similar in its action to the direct
coupled arrangement of Fig. 227. In either case, on account of the
coupling between the primary and secondary coils, there are re-
actions of each coil upon the other, with consequent double oscilla-
tions when the coils are near together. See Section 163. Sharp
296 RADIO COMMUNICATION.
tuning becomes impossible. It is found, however, that if the re-
sistance of the circuits ip low, extremely sharp tuning is obtained.
The antenna is tuned to the incoming waves by changes of the
inductance L^. Sometimes if very sharp primary tuning is desired,
a variable condenser is shunted around Li, and fine adjustments are
made therewith. The secondary is tuned to the primary, the opera-
tions of tuning being done alternately until the telephone gives the
best response. In the secondary the coarser tuning is done by
changes of the inductance -Lj, and the fine tuning with the variable
condenser C2.
Comparing Figs. 195 and 228, it will be found that the circuits are
the same. One finds in both places the antenna circuit (radiator or
absorber), the closed oscillating circuit, the coupling coils, and the
power inserted or detected in shunt connections to the condenser.
The main difference of apparatus is that instead of a high voltage
condenser as in Fig. 195, C2 is a small variable air condenser, and
instead of spaced-tum coils of large wire, the coils of the receiving
apparatus have many turns of insulated wire closely wound.
For receiving a longer wave in the primary circuit than is possible
by using all of the inductance L2 a series inductance £3, called a
loading coil, is added. See Fig. 229. Also, a variable condenser
may be connected as shown at C3 to increase the wave length and
afford fine tuning. The secondary may also be provided with an
extra inductance in series with L2 if needed. For receiving short
waves on a large antenna, series condenser C4 is inserted in the ground
wire. It is short circuited when not in use.
In the typical set of Fig. 228, a crystal rectifier (Section 179)
is used as the detector. The principal disadvantage of this type of
detector is that it can not be depended upon to stay in adjustment.
A good deal of time is required for the frequent readjustments.
Fig. 230 shows exactly the same connection, but with the crystal
detector replaced by a Fleming valve, F. This is a glass bulb
containing two electrodes and having the air exhausted. One
electrode in the vacuum is a lamp filament which is heated by
current from a storage battery A. The other electrode is a metal
plate. The heated filament gives off a stream of electrons (Section
184) toward the plate. Current from incoming electric waves can
pass through the vacuum in only one direction determined by the
electrons, the current in the opposite direction being suppressed.
RADIO COMMUNICATION.
297
In this way the tube acts as a rectifier. It is very stable and about
as sensitive as a good crystal.
A still further improvement is shown in Fig. 231, using a vacuum
tube having three electrodes. It is s*en here that the circuits
joined to the filament and the nearer electrode are exactly the same
as in Fig. 230. The telephone, however, is in a circuit with a bat-
tery Bf and the signals received thereby are much louder than in
the case of Fig. 230. For the theory of action of the three-electrode
vacuum tube as a detector see the next chapter, Section 191.
Ca-pacUively Coupled Receiving Set. — ^A method of coupling receiv-
ing apparatus to the antenna circuit which affords compactness
V
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r«e«ivir^ eireui't
is shown in Fig. 232. By fixing the primary and secondary coils
Li and L2 permanently at right angles to each other, inductive
coupling between the two is prevented. Instead, the coupling
between the two circuits is effected through the condensers CC,
which are referred to as ** coupling condensers." Such an arrange-
ment is called ** electrostatic" or **capacitive" coupling. The
condensers are arranged so that by turning one handle both are
varied together. One of the condensers, C, the one connected to
earth, may be omitted, but better results are usually obtained with
two. The advantages of capacitive coupling are as follows. (1) The
coils are of compact form. They are wound as rings with rectangu-
298
RADIO COMMUNICATION.
lar or square winding section, thus giving large inductances in
small space. This is a great saving of room compared with sets
using variable inductive coupling where the coils must be so con-
structed that one of them can move with respect to the other, and
where they are usually wound on long tubes in order to get suitable
variation of coupling. (2) The coils are fixed. In the inductive
type they must sometimes be separated many centimeters for very
loose coupling. (3) The coupling is quickly and easily changed.
Sets far Quick Tuning. — ^When simplicity of tuning is the principal
requirement) and it is desired to reduce the tuning operations to a
V
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Fio. 232
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Ho. 233
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minimiiTn number, even at the expense of a certain amount of
selectivity, the following methods are used.
In Fig. 233 is shown a modification of the capacitive connection
of Fig. 235; in practice the change from one to another is accom-
plished by one switch. The secondary is removed, and the tele-
phone is put in shimt with the detector instead of with the fixed
condenser FC. If a mediimi value of coupling is used it is not
usually necessary to alter it, therefore the only tuning adjustment
is that of the primary inductance.
Another device for quick tuning is shown in Fig. 234. This
employs an inductive coupling. The primary is tuned sharply to
the incoming waves, while the secondary is untuned. With the
connections as shown, the secondary will respond in practically the
RADIO COMMUNICATION.
299
same manner to a wide range of wave lengths, owing to the high
resistance of the detector. Then the only adjustment the operator
has to make is that of the primary inductance. Sometimes addi-
tional provision is made for adjustment of the coupling by separating
the coils; this gives variation in the sharpness of tuning and in the
signal strength.
^^ Standby^* Circuits. — ^These are also called "pick-up" circuits.
When listening for possible calls from a number of stations it is
convenient to have apparatus which will respond to a wide variety
of wave lengths. The circuit of Fig. 233 will do this to a limited
extent if the coupling is close. This is also true of Fig. 234. Prob-
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ably the most broadly tuned of all the receiving sets is the plain
aerial connection already shown in Fig. 224 or Fig. 225. It is,
however, too broadly tuned to be used if many stations are trans-
mitting.
A fairly good pick-up circuit is the ordinary inductive set of
Fig. 228 when used with a tight coupling. The decrement is then
high, and the tuning broad. A switch may be provided, if desired,
to put the receiving instruments over into the antenna circuit.
178. Circuits for the Reception of Undamped Waves.— While
damped waves are transmitted as detached groups or trains, un-
300 RADIO COMMUNICATION.
damped waves are usually not separated into groups. Undamped
waves, even if rectified, will not be detected in a telephone receiver
unless the waves are broken up into groups in some way. This is
because the telephone diaphragm and the ear cannot respond to so
high a frequency as that of the radio oscillations. Hence it is
necessary to interrupt the undamped wave dot or dash into many
groups by rapid interruptions of the current. It is arranged in
practice to have, for example, 1000 interruptions a second, and as
long as a signal continues a note of pitch 1000 is heard. These
interruptions may be made to take place either at the transmitter
or at the receiving station. A method for producing them at the
transmitting station is to insert a rapidly operating circuit breaker
called a *' chopper" in the antenna wire; or if it is inconvenient to
treak the current, the chopper may be used to short circuit some
of the turns of the antenna inductance coil to throw the circuits
out of resonance periodically. This divides up the waves into
groups to which the receiving telephone can respond. A rather
more convenient method is to have the chopping done at the receiv-
ing station, for then the receiving operator can control the pitch
of the received signals. There are at least five ways of modifying
the waves at a receiving station to obtain an audible frequency:
(1) a chopper in series with the detector and telephone; (2) a vari-
able condenser with rapidly rotating plates; (3) a **tikker" used
instead of a detector; (4) a *' heterodyne" in a separate circuit;
(5) an **autodyne" or vacuum tube device arranged so that the
detecting tube also produces the heterodyne action. The last
method is explained in Section 201.
Chopper. — This may be any device for rapidly making and break-
ing the current. It is inserted in the circuit of the detector and tel-
ephone as in the ordinary damped wave set of Fig. 228. It con-
sists of a rotating toothed wheel with a stationary contact touching
the successive teeth or a break controlled by an electrically operated
tuning fork, or it is sometimes a light high speed vibrator similar to
that of an electric bell.
Rotating Plate Condenser. — If the movable plates of the tuning
condenser Cg in Fig. 228 are rotated rapidly the apparatus will be
in tune once for each revolution. Each of these revolutions will
produce an impulse of the telephone diaphragm. The speed can be
adjusted so that the impulses will cause sounds while waves are
being received. In practice it is found best to keep part of the ca-
RADIO COMMUNICATION. 301
pacitance of the condenser Cg constant, and vary only a part of it.
If the main plates were rotated the apparatus would give sounds at
only a small sector of each revolution, near the resonance adjust-
ment. To accomplish a more prolonged train of impulses during
one revolution the adjustment can be held near resonance for a larger
proportion of the time if the rotating condenser is made very small,
and is put in parallel with Cj. The latter does not then rotate ex-
cept for ordinary hand tuning. The capacitance of C2 plus the max-
imum capacitance of the rotating condenser is adjusted to give res-
onance. The circuit is not far from this condition when the moving
plates are farthest apart, so that the signals affect the receiver during
a considerable portion of the revolution.
Tikher. — Seie Fig. 235. The tikker is usually a stationary fine wire
of steel or gold with its end running in the groove of a smooth, rota-
ting brass wheel. It is a slipping contact device. The wire does
not remain in perfect contact with the wheel, but owing to the slight
irr^ularities there are variations of contact, which in effect keep
making and breaking the circuit. With the tikker contact open,
suppose the secondary inductance and condenser C2 to be tuned to
resonance with the incoming waves. If now the tikker is closed
when C2 has any stated value of charge, some of the charge will be
given to the condenser C and furthermore the radio oscillations cease
because the addition of C throws the apparatus out of tune. When
the tikker is opened the condenser C discharges through the tele-
phone, and in the meantime the secondary oscillations build up
again, ready to give a charge over to C when the contact is closed.
In this manner the current impulses through the telephone are of
the same frequency as the operation of the tikker, and this can be
controlled by the speed of the wheel. The capacitance of C should
be about 1 mf d . No separate rectifier is needed . The tone obtained
is not musical, since Cg is charged to different potential differences
at the different times when the tikker closes, and the action depends
also upon somewhat irregular contact.
Heterodyne. — In this method an apparatus is arranged to produce
undamped electric oscillations in the receiving circuit, of nearly
the same frequency ais that of the waves which are being received,
and their combined action Ls made to affect the receiving telephone.
Beats are produced having a frequency equal to the difference of the
frequencies of the two waves. The connections are shown diagrama-
tically in Fig. 236. Any source of undamped or slightly damped
302 RADIO COMMUNICATION.
oscillations is connected at A: In the antenna circuit at jB is a
single turn or loop, coupled inductively to A. The antenna circuit
thus gets the effect of the oscillations from A as well as from the
incoming waves. Suppose those received have a frequency of
100,000, and the heterodyne A is adjusted to give a frequency of
99,000. As long as both act, the telephone will respond to a pitch of
1000 vibrations per second, which is of course audible. When the
incoming waves cease the heterodyne continues to act alone at
99,000 cycles, but is inaudible. Therefore signals are heard only
diuing the time when the incoming radio waves are received.
Receiving from a Radio Telephone Transmitter. — ^WTiile a radio
telephone transmitting apparatus operates on undamped waves it
is not necessary, or indeed permissible, to use a chopper, tikker,
or heterodyne at the receiving station. The transmitted waves are
modified or varied in intensity by the spoken sounds and these
sounds are reproduced in the telephone of the ordinary receiving
set such as is used for damped waves.
179. Crystal Detectors. — ^A very simple and convenient kind of
detector is obtained by the contact of two dissimilar solid sub-
stances, properly chosen. The number of substances which have
been found suitable for use in such detectors is large. This type of
detector is easily portable, but requires frequent adjustment and
is less sensitive than a vacuum tube. For field sets where a com-
pact and easily portable form of detector is required, the crystal
detector is very convenient. The use of crystal detectors is largely
confined to such work now, and even in the portable military sets is
rapidly giving way to the vaccuum tube detector.
Crystals. — ^Among the combinations of solid substances which
have been used as contact detectors may be mentioned silicon with
steel, carbon with steel and tellurium with aluminum. The most
important contact detectors, however, consist of crystals, natural
or artificial in contact with a metallic point. Examples of such
minerals are galena, iron pyrites, molybdenite, bomite, chalcopy-
rite, carborundum, silicon and zincite. The first three are respec^
tively lead sulphide, iron sulphide and molybdenum sulphide.
Bomite and chalcopyrite are combinations of the sulphides of cop-
per and iron. Carborundum is silicon carbide, formed in the electric
furnace. The fused metallic silicon commonly used is also an elec-
tric furnace product. Zincite is a natural red oxide of zinc.
Probably the three most widely used crystals are galena, silicon
and iron pyrites. Sensitive specimens of iron pyrites are more
RADIO COMMUNICATION. 303
difficult to find than ienaitive galena, but they usually retain their
sensitiveiiees for a longer time than galena. These sensitive pyrite
deteclora are often sold under the trade name of "FerroQ." The
detector sold under the name of "Periton" consista of a bomite
point in contact with a mass of zindt*. Fig. 237 shoira a silicon-
antimony detector; other detectors have this same general appear-
Propertieg. — In order to act ae a detector for radio signals a crystal
contact ahould either (1) allow more current to flow when a given
voltage ia applied in one direction than when it ie applied in the
Fto. 217.— One method ot mounting cryatal detectors.
opposite direi'tion, or (2) its conductivity should vary as different
voltages in the same direction are applied. Practically all detec-
tors formed by the contact of two dissimilar substances possess both
of theee properties, at least to a slight extent.
To make use of the latter property, a battery is required in series
with the crystal, as explained below. Some crystals, such as galena,
silicon and iron pyrit«a give about as good results as simple recti-
fiers as when the battery method is used. They are ordinarily used
without the battery, to simplify the apparatus.
304
RADIO COMMUNICATION.
Fiff. 238 shows a current- voltage characteristic curve for carborun-
dum in contact with a metal. The current flows much more readily
in one direction than in the other under equal but opposite emfs.
For example, under a constant impressed emf . of 10 volts in one di-
rection a current of 100 microamp. is obtained, while with the
voltage reversed the current is only 1 microamp. This illustrates
the property of * * unilateral conductivity, ' ' or rectification. Further-
more, as regards the second property, when the voltage is applied in
the direction giving the larger curreut, the conductivity (ratio of
10
238
«...
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/
t,f 1
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m
i
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.y
f
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s
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V
t
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•»
4T<H
a
"^ 1
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' 1
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C*Jrvm shewing Iha
CAfberundiunN el«t«Afer
lb eendudf in onm dioactie
Fia. 231
yVXAA" /XAAAA
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rs'
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A^^^-^
Time
^^^VAAA
TiVn*
i^ction of eryatal eUrhaetbr with boe»t«r ba1t«r^
current to voltage) increases as the voltage increases. This is shown,
by the right hand portion of the figure. The characteristic curve
of any ordinary metallic conductor would be a straight line.
Booster Battery. — In order to make use of the second property
namely the bending of the current-voltage characteristic, a local
or * * booster " battery is inserted in series with the crystal . Using the
battery makes the crystal operate at a voltage which corresponds
with the sharpest bend of the curve, so that a slight increase of volt-
RADIO COMMUNICATION. 305
age in one direction will produce a fairly large increase of current,
while an equal decrease of voltage on the crystal will produce a
relatively smaller decrease of current.
The application is made clear in Fig. 239. Suppose the crystal
used with a booster battery adjusted to supply 2 volts to the circuit.
Consider this circuit to be subjected to incoming electric waves
which produce a small emf., say 0.5 volts, periodically added and
subtracted. Curve a represents the voltage induced in the cir-
cuit by the incoming waves. The resultant voltage wave acting on
the crystal is at each instant two volts greater than the value of
the induced emf., and is represented by curve b. Under the instan-
taneous applied emf. of 1.5 volts, shown at point p in curve 6, the
crystal will allow a current of 2 microamp. to pass as shown in Fig.
239-c; for 2 volts in curve b a current of 4 microamp. will pass
as shown in Fig. 239-<j, and for 2.5 volts a current of 8 microamp.
will pass. Curve c represents the condition which would exist
in a circuit containing no inductance. The actual current wave
through the telephone, as smoothed out by the inductance of the
telephone and the other inductance of the circuit, is shown in
curve d. In this discussion the curves are shown for the case where
the incoming waves are undamped. The average value of the cur-
rent d is somewhat above 4 microamp. during the time the incoming
wave group is acting. Between groups it drops to just 4 microamp.
(with 2 volts applied). Thus the current comes in pulses which will
cause a sound to be emitted by the telephone. This sound will be
determined by the number of wave trains received per second.
These may be groups of damped waves, or continuous waves broken
up by a tikker.
180. Telephone Receivers.— The distinctive features of telephone
receivers for radio work are lightness of the moving parts and the
employment of a great many turns of wire around the magnet poles.
The lightness of the moving parts enables them to follow and respond
to rapid pulsations of current. The large number of turns of wire
causes a relatively large magnetic field to be produced by a feeble
current. The combined effect is to give a very sensitive receiving
device. Inasmuch as the size of wire used is always about the same
(around A.W.G. No. 40 copper), the amount of wire and therefore
the number of turns is usually specified indirectly by stating the
number of ohms of resistance in the coils. Telephone receivers of
fair sensitiveness for radio work have 1000 ohms in each receiver
97340°— 19 20
306 RADIO COMMUNICATION.
(measured on direct current), while the better ones usually have 1500
to 2000 ohms per receiver.
The most common type, called the magnetic diaphragm type, has
a U-shaped permanent magnet with soft iron poles, and a thin soft
iron diaphragm very close to the poles so that it vibrates when the
attraction is rapidly varied, producing sounds to correspond with the
frequency of the pulsations of current. See Section 60.
The only other important type is called a mica diaphragm receiver.
The regular diaphragm is of mica, and is put in the usual place in
the receiver, but of course is not acted upon directly by the magnets.
Between the magnet poles a soft iron annature is pivoted, inside of
a solenoidal telephone winding. It is arranged so that as it moves
in response to changes of magnetism a small stiff wire attachment
transmits the motion to the mica diaphragm. The armature is bo
arranged that there is no pull upon it at all except when pulsations
of current are passing through the coil. This is contrary to the ordi-
nary magnetic telephone receiver where the magnet poles are
always exerting a pull on the diaphragm. If there is no strain in
the diaphragm between pulsations the vibratory movements due to
incoming signals are much greater than if a strain were already
existing in the diaphragm or armature. In the mica telephone this
unrestrained vibration is communicated to the mica diaphragm near
the ear.*
Impedance. — ^The impedance of a telephone receiver to alternating
current increases rapidly with frequency, and at radio frequency is
so great as to permit practically no current to pass. By the use of
detectors, however, the current that passes in the telephone consists
of a series of pulses of audio frequency, usually from 500 to 1200
pulses or vibrations per second. A typical telephone receiver
having a direct current impedance (resistance) of 2000 ohms was
found at 400 cycles per second to have an impedance of 2900 ohms,
and at 800 cycles an impedance of 3900 ohms, rising to 4400 ohms
at 1000 cycles per second.
181. Receiving Coils and Condensers. — ^The coils used in receiv-
ing apparatus are very simple in construction, being usually wound
in a single layer of wire on a bakelite, pasteboard, or other insulating
tube. The wire is usually stranded and covered with an insulation
of silk or cotton. In some types one or two sliders make contact
with any desired turn of wire, the insulation being scraped off on
1 For a detailed account and tracing out of the magnetic circuits see Bucher's Prac-
tical Wireless Telegraphy, page 168.
RADIO COMMUNICATION.
307
top of the wires along a narrow path lengthwise of the coil. The
more common field sets use no slider but have switches whose points
are connected by tap wires to the turns of wire in the coil. One
switch takes care of single turns, and the other switch makes contact
to groups of, say, ten turns each. To cover 100 turns, for instance,
one switch should have 9 points of ten turns each, and a zero point,
making 10 points in all, and the units switch would also have 9 points,
7m? Type J of ^ecety'r*^ //&. ^4^0
L
and a zero point. Then any number from to 100 turns could be
used. If a coil had 400 turns the first switch in groups of 20 turns
could have 20 points including zero, and the unit switch could also
have 20 points for nineteen unit turns and zero.
Fig. 240 shows two receiving transformers, in one of which the
primary adjustment is made by a slider touching each turn of wire,
and the secondary adjustment is made by a switch in groups of 30
308 BADIO COMUVN
to 40 tuniB. The finer secondary tuning is done by a variable con-
denaer. The coupling between the coile is loosened by pulling the
secondary out of the primary. The other receiving transformer has
control of both coils by Bwitchee.
Loading coila are merely large coils used to increase the induc-
tance of the circuit when the inductance of the receiving transformer
is not great enough to be tuned to the wave length received. Ordi-
nary tuning coils and the eoils of receiving transformora of the
inductively coupled type are usually 12 to 20 cm. long and 8 to 12
cm. in diameter, with single layer windings, while some of the com-
F:o. Ml.— Rotary varisble air condenser,
inon loading coils (or long waves are 50 cm. or more in length. The
inductance of the 12 cm. coils runs from 1000 to 5000 microhenries,
while the large loading coils have in the neighborhood ol 60 milli-
henries. The inductance of any particular coil can be calculated
by reference to Section 170.
Fig. 241 shows a type of variable condenser with air dielectric,
which is generally used. The maximum capacitance is usually
0.0005 mfd., adjustable to a'minimum of nearly zero. A set of semi-
circular metal plates is rotated between a corresponding set of fixed
nADlO COMMUNICATION, 309
plates, forming alternate layers of air dielectric with adjacent con-
ductors of oppoeite polarity. In working with vacuum tubes meet
of the tuning is done with variable condensetB. In the primary
it sometimeB happens that, with continuouB waves, the tuning must
FiQ. 312.— Simple recclvliig set {type &CIt-S4-A) ol the porlabEo, cabinet type-
be closer than that afforded by single turns of the primary coil, so a
variable condenser is placed in parallel with the coil and used for
fine tuniug.
Fig. 242 shows a typical simple receiving set in cabinet form,
with the tap switches and variable condensers, and a handle for
changing the coupling between primary and secondary coils.
310 RADIO COMMUNICATION.
182. Measurement of Beceived Current. — It is possible to measure
current received in a radio receiving set by the use of a crystal
detector and a galvanometer. This is a rather delicate experiment,
and information regarding it is given in C. 74, pages 167 to 170. The
method ordinarily used is the shunted telephone method. A resis-
tance is placed in parallel with the telephone and reduced until the
limit of audibility in the telephone is reached, that is, until the
sound in the telephone becomes so weak that the operator can just
barely distinguish dots and dashes. If t is the impedance of the
telephone for the frequency of the current impulses through it, s the
impedance of the shunt. It the least cmrent in the telephone which
gives an audible sound, and /the total current flowing in the com-
bination of the telephone and shunt,
I_8+t
ir s
This ratio, «+ 1 to «, is called the ' ' audibility. ' ' It can be expressed
in units of current if properly calibrated. It is ordinarily used in
making rough comparative measurements. It is, of coiu'se, affected
by the sensitiveness of the operator's ear.
For detecting currents of the order of 0.0001 amp., the crystal
detector and telephone are used; for 0.000001 amp., the ordinary
vacuum tube and telephone are used; for 0.00000001 amp., the
vacuum tube connected for regenerative amplification and telephone
are used.
CHAPTER 6.
VACUUM TUBES IN RADIO COMMUNICATION.^
183. Introduction. — ^The advent of vacuum tubes, sometimes called
electron tubes, has resulted in great advances in radio communica^
tion. As such tubes may be used for a variety of purposes, to gener-
ate, to amplify, and to modulate radio oscillations, as well as to
detect them, they are now used in most types of radio apparatus.
New applications have come rapidly, and possibilities of further
developments are most promising. One fact of importance is that
such tubes make possible the use of apparatus that is easily porta-
ble — a primary consideration in military conununication. The
principles underlying the uses of vacuum tubes, and their operation
under the widely different conditions met in actual practice, there-
fore deserve careful study.
A. Electron Flow in Vacuum Tubes.
184. Current in a Two-Electrode Tube. — If two wires are con-
nected to a battery, one to each terminal, the other ends may be
brought very close together, in air, yet so long as they do not touch,
no current flows between them. The two ends may be enclosed in a
bulb like that of an incandescent lamp, and the air pumped out,
leaving a vacuum, and still so long as the ends are separated, no cur-
rent flows. A common experience illustrates this. When the fila-
ment in an electric lamp breaks, the current stops and the light goes
out. But if one of the two wire ends mentioned above is heated to a
bright red, or hotter, it is an interesting fact that a current can be
made to flow across the apparently empty space between them.
Call the two ends of wire the "electrodes." The current between
the hot and the cold electrode is made possible by the electrons given
off by the hot electrode (explained further in the next paragraph),
and is a large enough current to be measured by sensitive instru-
ments and to have highly important uses in radio commimication.
1 See also S. C. Radio Pamphlet No. 1, Part 2.
311
312 RADIO COMMUNICATION.
The question will perhaps arise as to how a single electrode can be
heated when it is inside of a glass bulb. That is readily done by
shaping it into a loop, of which both ends are brought through the
base of the bulb . These ends are connected to a battery of a few cells,
the current from which heats the loop like an ordinary incandescent
lamp filament. Thus one of the electrodes becomes a hot filament.
For the other electrode a little plate of metal is used. A bulb con-
taining a hot and a cold electrode as described formis a "two-elec-
trode vacuum tube."
The action of these vacuum tubes depends upon the fact that
when a metal is heated in a vacuum it gives off electrons into the
surrounding space. (See Section 6.) As the electrons have a nega-
tive charge, the charge remaining on the metal is positive, therefore
few of the electrons go very far, but are attracted back to the metal
so that there is a kind of balance established between the outgoing
and the returning electrons. Now suppose a battery is connected
between the two electrodes, filament and plate. This battery is B
in Fig. 243, and is so connected as to make the plate potential posi-
tive with respect to the filament. The electrons, consisting of
negative electricity, are attracted by the plate P, are captured by
by it, and return no more to the filament F, Thus the battery
causes a continuous flow of electrons (negative electricity) from the
filament to the plate; that is, an electric current is flowing in the
space between them.
The current ceases when the filament is cold, becaiise no electrons
are then escaping from the metal. No current will flow if the battery
is wrongly connected, since, when the plate is negative with respect
to the filament, the negative charge of the plate will repel the
electrons back into the filament.
The distinction between direction of current and direction of
electron flow must be carefully noted. It happens that for a great
many years the direction from the positive toward the negative
terminal has been arbitrarily called the direction of the ciurent.
Now it is found that these little electrons travel from the negative
toward the positive electrode. The direction of current and the
direction of motion of the electrons are therefore opposite.
Ionization. — ^The above explanation of the mechanism of the
flow of ciurent between the filament and plate (commonly called
the *' plate current") in a vacuum tube applies to the case where
RADIO COMMUNICATION.
313
the vacuum is very complete. If there is more than the merest
trace of gas remaining in the tube, the operation is more complicated,
and a larger cmrent will usually flow with the same applied voltage.
This happens in the following manner.
In a rarefied gas, some of the electrons present are constituent
parts of atoms and some are free. These free electrons move about
F»a. 243
#ltt|i|i|H
Two««leetrod«
Afdcuum tvb«
F - FilAm«pt
P - PU+«
A- CaTtery f«r hcAtiir^
XllAtnent
5- &«Ttery for a«iWir^
currerit -fhno «^i*e« b^tWmmn
^bdk And fUment
FlO. Z44
,.-''r^^.Tt
PUU Vclt>^ <
ChAnAetsri'atio eurv«» of Atw«<
•loetroJo, tub* for tWe diffanortf
/'VoltA«> V«
'/^^^•My
FiO.245
>T TWm^iifctor^
ChAMcieristic curved of 4 two*
•Ueirod* ti/b« -for two di/(er«nt
with great velocity, and if one of them strikes an atom, it may dis-
lodge another electron from the atom. Under the action of the emf.
between plate and filament, the newly freed electron will acquire
velocity in one direction (that of the colliding electron) and the
314 RADIO COMMUNICATION.
positively charged remainder of the atom will move in the opposite
direction. Thus both of the parts of the disrupted atom become
carriers of electricity and contribute to the flow of current through
the gas. This action of a colliding electron upon an atom is called
*' ionization by collision", and on account of it relatively large plate
currents are obtained in vacuum tubes having a poor vacuum.
The earlier *'audion" tubes were of this sort, but tubes are now, as
a rule, made with better vacua than formerly, so that ionization
by collision is responsible for but a small part of the current flow.
At first it would seem to be an advantage to have ionization by
collision, because a larger plate current can be obtained, but there
are two difficulties which have proved so great that tubes are now
usually made to have only the pure electron flow. The first of
these dificulties is a rapid deterioration of the filament when a
large plate current flows. The positively charged parts of the
atoms are driven violently against the negatively charged filament,
and since they are much more massive than electrons (an oxygen
or nitrogen ion has about 25,000 times the mass of an electron) this
bombardment actually seems to tear away the surface of the fila-
ment. The second disadvantage of tubes with poor vacuum is
that too large a battery voltage may cause a **blue glow" discharge;
the difiiculties connected with the presence of this visible kind of
current flow are mentioned in Section 191.
185. Actual Forms of Two-Electrode Tubes. — ^A tube similar to
that described above was the earliest used in radio practice. It
was called the "Fleming valve." It rectifies a high-frequency
current somewhat as a crystal detector (Section 179) does. This
rectifying action takes place because a current flows when the
negative terminal of a battery is applied to the heated filament
and the positive one to the plate, whereas the current becomes
practically zero if the battery connection is reversed. The latter
happens because the negatively charged plate repels the negative
electrons and stops the current flow. The Fleming valve was used
as a detector, but has been replaced by the three-electrode tube
discussed below because the latter has proved to be much more
sensitive.
Another type of two-electrode tube is the "kenotron," developed
by the General Electric Co. It has a much better vacuum than
the Fleming valve, and is made in larger dimensions. It is used as
a rectifier of currents of high voltage and low frequency. It changes
RADIO COMMUNICATION. 315
alternating current into a pulsating current all in one direction.
Small currents (well below 1 amp.) are rectified by these tubes, and
power up to several kilowatts can be handled even if the applied
voltage exceeds 25,000.
A third form of two-electrode tube, which promises to be useful
for military purposes, is the "tungar rectifier." ^ These tubes con-
tain rarefied argon gas and their relatively large currents are pro-
duced mainly through ionization by collision. These are useful for
charging storage batteries from a 110- volt a.c. line. One size charges
a battery of from 6 to 12 volts at from 1 to 2 amp. ; a larger size charges
a 6 or 12 volt battery at 6 amp.
186. The Three-Electrode Vacuum Tube. — ^A great improvement
upon the two-electrode tube for radio purposes, consists in the addi-
tion of a third electrode, inside the tube, in the form of a metallic
gauze or *'grid" of fine wires between the filament and the plate.
This makes it possible to increase or decrease the current between
plate and filament through wide limits. It is important to under-
stand how this result is obtained.
It is necessary first to consider what happens in a two-electrode
tube having a good vacuum, when either the voltage of the battery
B or the temperature of the filament is varied.
Effect of Plate Voltage, — Suppose first that the filament tempera-
ture is kept constant. Then a definite number of electrons will be
sent out per second.* The number of electrons that travel across
the tube and reach the plate per second determines the magnitude
of the current through the plate circuit. The number of electrons
that reach the plate increases as the voltage of the battery B in-
creases. If this voltage is continuously increased, a value will be
reached at which all the electrons sent out from the filament arrive
at the plate. No further increase of current is possible by increasing
the voltage and this ciurent is called the saturation current. This
is illustrated in Fig. 244, (full line curve) which shows that when
the voltage applied to the plate is small, (horizontal distance) the
current flowing between filament and plate, called the *' plate cur-
rent" (vertical distance) is also small, but if the voltage is made
1 R. E. Russell— General Electric Review, 20, p. 209; 1917.
s The law giving the number of electrons emitted per second, as it depends upon
the temperature of the filament, was first given by O. W. Richardson, whose book,
"The Emission of Electricity from Hot Bodies" (1916) describes his experiments in
great detail. See also J. J. Thomson, "Conduction of Electricity through Gases,"
p. 161, and I. Langmvir, Physical Review, 2, p. 450; 1913.
316 RADIO COMMUNICATION.
larger, the plate current increases more rapidly than the voltage,
up to a certain value. The bend in the curve shows that when the
voltage has been made large enough, there is little further gain in
current.
If now the temperature of the filament is raised by means of the
heating battery to a higher constant value and the same voltage
steps again applied, the plate current curve will coincide with that
obtained before, until the bend is reached, then it will rise higher,
as shown by the dotted portion of the curve in the Fig. 244. The
explanation of this is that the number of electrons sent out by the
filament increases with the temperature, approximately as the
square of the excess of filament temperature above red heat, and
thus more are available to be drawn over to the plate. Thus a
higher value of plate current will be obtained before reaching the
limiting condition when all the electrons emitted arrive at the
plate. When this finally happens the curve, as before, bends over
until nearly horizontal.
Effect of Filament Temperature. — Suppose now that the voltage
of battery B is kept at a constant value Fj, and the filament tempera-
ture gradually raised by increasing the current from the heating
battery. The number of electrons sent out will continue to increase
as the temperature rises. The electric field intensity (Section 33)
due to the presence of the negative electrons in the space between
filament and plate may at last equal and neutralize that due to the
positive potential of the plate so that there is no force acting on the
electrons near the filament. This effect of the electrons in the
space is called the "space charge effect." It must not be sup-
posed that the space charge effect is caused by the same electrons all
the time. Electrons near the plate are constantly entering it, but
new electrons emitted by the filament are entering the space, bo
that the total number between filament and plate remains constant
at a given temperature. After the temperature of the filament has
reached the point where the effect of the electrons present in the
space between filament and plate neutralizes the effect of the plate
voltage, any further increase of the filament temperature is unable
to cause an increase of the current. The tendency of the filament to
emit more electrons per second, because of the increased tempera-
ture, is offset by the increase in space charge effect, which would
result if electrons were emitted more rapidly; or, more exactly, for
any extra electrons emitted, an equal number of those in the space
are repelled back into the filament. If now the plate voltage is in-
RADIO COMMUNICATION. 317
creased to a new value Fj, the plate current ciu^e will rise higher
before bending over as shown by the dotted portion of the curve in
Fig. 245, because it takes a larger space charge to offset the effect
of the plate at the higher voltage.
187. Effect of Grid. — In the three-electrode tube, the additional
electrode, or grid, is interposed between filament and plate, in the
stream of electrons which constitute the plate current. If a voltage
is impressed upon it by means of a third battery, shown at C in Fig.
246, this modifies the space charge effect. The electrons traveling
from filament to plate pass between the grid wires. If the grid
is given a potential more negative than the filament, it will repel
the electrons, but many of them will still pass through, owing to their
high velocity, and reach the plate. If the grid potential is made
still more negative, the plate current will diminish until finally it
may be stopped completely.
Suppose, however, the grid is given a positive potential instead
of negative. More electrons are now drawn toward the plate than
would otherwise pass, and the plate current increases. The grid
charge partially neutralizes the effect of the space charge. As in
the two-electrode tube, a limit to the magnitude of the plate
current will finally be reached, when the space charge due
to the large number of negative electrons in the tube, fully coun-
teracts the influence of the positive charges on grid and plate.
The attainment of the limiting or saturation value of the plate current
is assisted by the absorption of more electrons into the grid if its
positive potential is increased. This absorption gives rise to a
very small current in the circuit FGCF (Fig. 246) which is called
the grid ciurent. The total electron flow is the sum of the plate
current and the grid current. As the potential of the grid is made
more and more positive, more and more electrons will be absorbed.
188. Characteristic Curves. — ^The above principles may be illus-
trated by curves obtained by experiment, known as the character-
istic curves of a vacuum tube.
One form of these curves shows the relation between plate current
and grid voltage. For example, a certain tube was tested by keep-
ing the filament at a constant temperature by a steady current
through it from battery A (Fig. 246). A constant voltage of 35 volts
between plate and filament was maintained by the battery 5, and
varying voltages from to 7 volts were applied to the grid G by the
battery C. For each value of grid voltage the current flowing
318
RADIO COMMUNICATION.
between filament and plate was noted in the microammeter M.
The result is plotted in Fig. 247 and in the upper curve of Fig. 248.
It shows that as the grid voltage increases from —3 to +7 volts,
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the plate current increases from zero, slowly at first, then more
rapidly, but above 2 volts more slowly again. Similar tests with
lower plate voltages, 30 volts and 25 volts respectively, gave similar
RADIO COMMUNICATION. 319
results except that the plate currents were smaller, as shown in the
two other full line curves of Fig. 248.
Another important characteristic curve shows the relation between
grid current and grid voltage. This curve is also shown in Figs.
247 and 248. It is at once evident that the grid current is very small
in comparison with the plate current. In order to get a clearer
idea of the dependence of the grid current on the grid voltage, it
is customary to draw the grid current to a magnified scale. For
example, the grid current measurements made in the above men-
tioned case when the plate voltage was held at 30 volts, are shown
in Fig. 248 to such a scale that the same vertical distance which
represents 200 microamp. of plate current indicates only 5 microamp.
of grid current. Note that the grid current is zero for a very small
n^ative grid voltage, but rapidly increases with increasing posi-
tive grid voltage.
189. Effect of an Alternating Emf . Applied to Grid. — It is evident
from these curves that if an alternating emf. is applied to the grid
(that is, if it ifl made alternately -f- and — ), the plate current will
periodically increase and decrease, keeping step with the variations
in grid emf. Suppose the grid potential to be the same as that of
the filament (grid voltage zero in Fig. 246) the upper curve of the
figure shows that the value of the plate current will be 100 microamp.
when there are 35 volts on the plate. Then if an alternating emf.
of 1 volt (maximum value) is impressed between grid and filament,
the plate current will keep changing from the value of the ordi-
nate of point b (Fig. 248) to that of point c, that is, from about 260
to about 50 microamp.
Thus an increase of one volt in the emf. applied to the grid
produces an increase in the plate current of 150 milliamp. (from
100 to 250), while a decrease of the same amount in grid voltage
causes a reduction of only 50 milliamp. The effect then of applying
a high frequency oscillating voltage to the grid will be to cause a
higher "average" value of plate current during the time of such
voltage application. The preceding discussion relates to what
happens when the points a, 6, and c are on the lower bend of the
characteristic curve. When the grid voltage is so adjusted that
the plate current has a value somewhere on the upper bend of the
characteristic curve, the effect of applying an oscillating voltage
to the grid will again be to cause oscillations of the plate current.
Here, however, the effect of the alternating grid voltage is to cause
320 RADIO COMMUNICATION.
a "lower'* average value of the plate current. If the grid voltage
is adjusted to such a value that the plate current assumes a value
on the straight portion of the characteristic (say point P, Fig. 247),
oscillations of the grid voltage cause oscillations of the plate current^
but the average value of the plate current is, in this case, unchanged.
These facts are shown in Fig. 249. At the left is represented the
plate characteristic, and three points Ay B, and C are designated,
on the lower bend, straight portion and upper bend, respectively.
To the right is shown the effect of an alternating grid voltage in
each case. The dotted lines represent the original values of the plate
current. The full curves show the oscillations of plate current, caused
by the oscillations of the grid voltage, and the full straight lines
the average plate current during these oscillations. As will be shown
later, cases A and C represent conditions suitable for use of the tube
as a detector, and B the condition for use as an amplifier. There
is no appreciable time lag between grid voltage and plate current
and thus no phase difference, even when the frequency of i^lter-
nation is several million per second.
With different kinds of tubes different values of the grid voltage
are necessary, in order to obtain a value of plate current at the
desired part of the characteristic. This adjustment is accom-
plished by the C battery in the grid circuit (Fig. 246). Since the
plate current is so sensitive to small changes of grid voltage, it is
often desirable to provide a voltage divider on the C battery to
facilitate the close adjustment of the grid voltage. In C. 74,
p. 203, is illustrated such an arrangement which is useful in
experimental determinations of the characteristic curves.
190. Practical Forms of Three-Electrode Tubes.^ — In Fig. 250 are
shown a nimiber of French and American tubes. Those in (A) are
French. The two smallest tubes are the ones most commonly used;
they serve for detectors, amplifiers, and generators. The one with
two projections is used for short wave length apparatus, the idea
of the construction being to keep the connections to grid and plate
as widely separated as possible, to minimize capacitance between
them. Both types have a straight filament, the grid is a spiral wire
surrounding the filament, and the plate is a cylinder surrounding
both. A number of Western Electric Co. tubes are shown in (B)
General Electric Co. tubes (called by that company "pliotrons'*)
in (C), and DeForest Radio Telephone and Telegraph Co. tubes
(called by that company "audions") in (D). The DeForest Co.
1 See also Electrical World for Feb. 22, 1919, Vol. 73, No. 8; article by Capt. Ralph
Bown.
Fig. 250.— French and American vacuum tubes.
97340" — 19 21
321
322
RADIO COMMUNICATION.
makes larger tubes, called '^oscillions.*' In all modem American
tubes the filament is a wire doubled back one or more times; the
grid is a pair of metal lattices, one on each side of the filament;
and the plate is a pair of metal planes parallel to the two parts of
the grid. The larger tubes are used as generators of radio current
B. The Vacuum Tube as a Detector.
191. Simple Detector Circuit and Explanation of its Action. — In
order to understand how a vacuum tube acts when used as a detector,
consider the circuit shown in Fig. 251. Suppose the receiving
antenna picks up a signal. Oscillations in the tuned circuit LCi are
set up, because L is inductively coupled to the antenna circuit. The
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radio frequency alternating voltage between the terminals of Z is
impressed between the filament and the grid, and (as was explained
in Section 189) brings about changes in the plate current. If the
plate current is normally at a point on the bend of the characteristic
curve, say in the region a to c. Fig. 248, the increase of plate current
when the grid voltage is positive is greater than the decrease of plate
current when the grid voltage is negative. On the average the plate
current is increased while the signal is passing. Fig. 252 shows
graphically the simultaneous values of (1) high frequency oscilla-
tions of the grid current, (2) high frequency variations of plate cur-
rent, and (3) audio frequency fluctuations of telephone cturent.
The frequency of the wave trains should be within the range of
RADIO COMMUNICATION. 323
audible sound, preferably between 300 and 2000, because the tele-
phone inductance smooths out each train of high frequency oscil-
lations into a single pulse and the pulse frequency must, therefore,
be within the audible range in order that the signals may be heard.
In some cases it is necessary to use a C battery between points/
and g (Fig. 251), in order to bring the plate current to the bend of
the characteristic curve (Fig. 248). This, however, does not change
the action; the variations of the plate current are brought about by
the alternating emf . between the terminals of the coil L just the same
as when the C battery is absent. It is interesting to note here that
we are employing resonance in the circuit LCi to obtain as large
an emf. as possible between the terminals of the coil and condenser
with a given signal (see Section 109).
If the grid battery voltage is adjusted so that the plate current has
a value near the upper bend of the plate current-grid voltage curve
instead of the lower bend, the action will be essentially the same,
but the effect of the arrival of a wave train will be to decrease
momentarily the plate current instead of to increase it. As before,
there will be fluctuations of the plate current keeping time with the
arrival of wave trains, and a sound in the telephone of a pitch cor-
responding to the number of wave trains per second.
Care must be taken in the use of receiving tubes that the B battery
voltage is never high enough to cause the visible ''blue glow" re-
ferred to in Section 184. The tube becomes very erratic in behavior,
when in this condition, and is very uncertain and is not sensitive
as a receiver. This is because the plate current becomes so large
that it is imaffected by variations of the grid voltage. Characteristic
curves will not repeat themselves if the tube shows the blue glow
and sharp breaks may appear in any or all of the curves. Further-
more the tube gets hot and its safety is endangered by the blue glow
discharge.
Condenser in Grid Lead. — If the circuit of Fig. 253 is used, having
a condenser in series with the grid, the action of the tube as a detector
is different. It now depends upon the form of the grid voltage —
grid current curve (dotted curve of Fig. 248). When the grid voltage
is the same as that of the filament and there are no grid oscillations.
Fig. 248 indicates that under these conditions the grid current is zero;
that is, no electrons are passing from filament to grid. Now suppose
324
RADIO COXHUNICATIOK.
thftt a series of wave traiiis falln upon the antenna of Fig. 253 as shown
in n ; of Fig. 254, If the circuit L Q is tuned to the same wave length
as the anUfnna cirruit, oscillations will b? set up in it, and Himilar
CD
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stopping condenser C2.* Each time the grid becomes positive, elec-
> A suitable value for the capadtanoe of the oondenser Ct is about 0.0001 mfd.
RADIO COMMUNICATION. 325
trons will flow to it, but during the negative half of each oscillation
no appreciable grid current will flow. This is shown in curve (2) of
Fig. 254. Thus during each wave train the grid will continue gain-
ing negative charge and its average potential will fall as shown in (3)
of the same figure. This negative charge on the grid opposes the
flow of electrons from filament to plate, causing on the whole, a
decrease in the plate current. At the end of each wave train this
charge leaks off through either the condenser or the walls of the tube
(or both), and the plate current rises again to its normal value as
shown in (4) of the same figure. This should happen before the next
wave train comes along, but sometimes the leaJc is not fast enough
for this discharge to take place. In this case a better result is
secured if a resistance of a megohm or so is shunted across the con-
denser. Such a resistance is called a * ' grid leak . ' '
The telephone diaphragm cannot viebrate at radio frequency but
the high inductance of its coils smooths out the plate current varia-
tions into some such form as is shown at (5) in the figure. Thus as in
the case of the circuit of Fig. 251, the note heard in the telephone
corresponds in pitch with the frequency of the wave trains. If the
waves falling upon the antenna are undamped waves they may be
detected using either of these circuits, if they are first divided off
into audio frequency groups. (For methods see Chapter 7, Section
178). To receive undamped waves which are not divided up into
groups of audible frequency, vacuimi tubes may be used in special
ways called the heterodyne and autodyne methods. See Section
201 below.
192. Effect of Incoming Signals upon the Plate Current. — ^The
theory of detector action just given involves a change in both the
plate current and grid current of the receiving tube. It is easily
shown experimentally that such changes take place. The result of
one such experiment is shown in Fig. 255. The solid line curve is
similar to those of Fig. 248 and shows for a particular tube with a
constant plate voltage the values of plate current for various values
of grid voltage between —5.5 and +5.5 volts. The lower (dotted)
curve shows how much the plate current changed when a signal
was being received. The circuit was so arranged that the effect
of the signal was to add a high-frequency oscillating voltage
to the adjustable steady voltage applied to the grid, as ex-
plained in Section 191. The height of the dotted curve shows, for
326 RADIO COMMUNICATION.
each value of grid voltage, how much the plate current was changed
by the signal. It will be noted that in some cases the effect is an
increase of plate current, but in other cases a decrease corresponding
to the different parts of the plate current curve, as explained in Sec-
tion 189. Thus when the steady voltage applied was +1.1 volts,
the plate current was increased by about 35 microamp., and when
the voltage was zero, by 70 microamp. With +1.3 volts applied
there was no change at all in the plate current when the signal came
in, while for +5 volts there was a decrease of more than 100 micro-
amp. produced by the same strength of signal. Since it is the plate
current that passes through the telephone receiver it is evident that
with this particular tube the signals received are clearest with zero
or about 5 volts positive applied to the grid, but 1 to 1.5 volts should
be particularly avoided. Different tubes show similar results but
the voltage values differ somewhat.
The tubes generally supplied to the Signal Corps for receiving
(types VT-1, VT-11 and VT-21) are all so designed that they operate
to good advantage — like the tube considered above — ^when the grid
is kept at the same voltage as the negative end of the filament, that
is, grid voltage zero.
C. The Vacuum Tube as an Amplifier.
193. General Principle. — It was shown in Section 191 that a vac-
uum tube acts as a detector or rectifier because an alternating volt-
age applied to the grid circuit can be made to produce unsymmetri-
cal oscillations in the plate circuit. While the tube is thus acting
as a detector, it is also as a matter of fact acting as an amplifier. That
is, greater oscillations are produced in the plate circuit for a given
alternating voltage in the grid circuit than would be produced by
the same voltage directly in the plate circuit. This explains why
the vacuum tube is a more sensitive detector than the crystal detec-
tor, which acts as a rectifier only.
It is sometimes desired to amplify an alternating current without
any rectifying or detecting action. This is done by keeping a voltage
on the grid of such value that the symmetry of the oscillations in
the plate circuit is not altered. Thus if there is a steady voltage
applied on the grid of such value that the plate current is on the part
of the characteristic curve that is practically straight (as point P
in Fig. 256) then a small change in grid voltage in either direction
causes the plate cmrent to increase or decrease by the same amount.
RADIO COMMUNICATION. 327
For instance, if the grid voltage is increased from v to Wy (Fig. 256)
or decreased by an equal amount from v to w, the current will, in the
first case, increase from a to c and in the second fall off by an equal
amount, from a to 6. In other words the wave form of the grid
voltage variation will be repeated in the fluctuating plate cur-
rent. The latter will now be equivalent to an alternating current
superinposed upon the steady plate current from the B battery.
The magnitude of the alternating current part of the plate current
will be greater, the steeper the slope of the curve at the point P.
The power expanded in maintaining the oscillations in the grid
current is far less than that involved in the corresponding plate
current change, because the grid current is much smaller than the
plate current and the voltage is also less. For example, referring
to the vacuum tube whose characteristic curves are given in Fig.
248, if the grid voltage oscillates so that the plate current fluctuates
between the values a and 6, the grid current changes from about 1 to 2
microamp., average voltage 2.2 volts. The corresponding change in
plate current is from 300 to 400 microamp., with average voltage
perhaps 35 volts. Remembering that amperes X volts = watts, we
have in the grid circuit a power expenditure of 2.2 microwatts and
in the plate circuit a corresponding power change of 3600 microwatts.
This much increased power is drawn from the energy stored in the B
battery. The signals may be thought of as exerting a sort of relay
action on the plate circuit, causing magnified power to be drawn
from the B battery. The tube is said in this case to act as an "am-
plifier." The variations of current in the grid circuit have been
compared to the slide valve of an engine since they admit energy
from the battery into the plate circuit, much as the slide valve
admits heat energy into the cylinder of the engine.
To utilize the amplified alternating current in the plate circuit,
the primary of a transformer T (Fig. 257), may be placed in the plate
circuit. From the secondary of this transformer, the alternating
current (see Section 60) is delivered to a crystal detector or other
receiver; or, if further amplification is desirable, to the grid circuit
of a second amplifing tube, as shown in Fig. 257. From this second
tube it then goes to a receiving tube or crystal. This method of using
two or more tubes for amplification is called cascade amplification.
Instead of passing on the amplified energy by means of a trans-
former coupling, the coupling may be simply a resistance or a react-
ance. An example of this is shown in Fig. 258 where a crystal
328 RADIO COMMTJN
detector is shown as the receiver. To get the greatest power output
from the tube ft resiBtance should be used in the plate circuit of a
value equal to the average istemal reaistance of the tube, just aa
in the case of a direct current generator of cousttuit voltage, the great-
eat power outpi^t occurs when the internal resistance equals the
external.
194. ElementaTy Theory of Amplification.— The characteristic
a tube show that an increase in the grid voltage
RADIO COMMUNICATION. 329
makes a much greater increase in the plate current than the same in-
crease in the plate voltage itself would do. Consider, for instance, the
two upper curves of Fig. 248, p. 318. From the curve marked **30
volts " we see that the plate current increases from 200 to 400 micro-
amp, when the grid voltage is increased from 1.2 to 3 volts, or 110
microamp. per volt change. If on the other hand, the grid voltage is
left unchanged at 1.2 volts and the plate voltage increased to 35 volts,
the upper curve shows that the plate current increases to 280 micro-
amp.; a change of 80, or 16 microamp. for each volt. In other
words a volt added to the grid voltage makes about 7 times as much
change in the plate current as a volt added to the plate voltage
would make. This number which represents the relative effects of
grid voltage and plate voltage upon plate current is called the **am»
plification constant" of the tube.^ The greater this amplification
constant is, the more efficient is the tube as an amplifier of weak
signals. It may be defined as the ratio of the change in plate current
per volt on the grid to the change in plate current per volt on the
plate.
The two principal constants of a tube are the amplification con-
stant just defined and the internal resistance. The latter is the
resistance to an alternating current between plate and filament in
the tube. These two constants may be calculated from the char-
acteristic curves of the tube, or may be measured by a simple method
like a bridge measurement. ^ The voltage amplification given by
an amplifying circuit may be calculated from these two constants
of the vacuum tube.
The voltage amplification may be defined as the ratio of the voltage
change produced in the output apparatus in the plate circuit to
the change in the voltage impressed on the grid. Thus in the re-
sistance coupled amplifier, of Fig. 258, it is the ratio of the voltage
between a^ and 6^ at the terminals of R to the voltage applied be-
tween a and 6. Calling the amplification constant jSTand the internal
resistance i?o, it can be shown that the voltage amplification for such
an amplifier is
KR
R-\-R,
1 The theory of amplification has been worked out in more detail by Langmuir,
Proc. Inst. Radio Engineers, 3, p. 261, 1915; by Vallauri, L'Elettrotecnica, 3, p.
43, 1917; and by H. J. Van der Bijl, Physical Review, 12, p. 171, 1918.
8 For information on such measurements see papers, by J. M. Miller, Proceedings
Institute of Radio Engineers, 6, p. 141, 1918; and H. J. Van der Bijl, Physical Review,
12, p. 171, 1918.
330 RADIO COMMUNICATION.
195. Audio Frequency Amplification. — ^In the preceding discussion
of amplification, it was pointed out that after a radio frequency cur-
rent is amplified it is passed through some rectifying device. This
latter is not necessary when an audio frequency current is amplified,
for the amplified current can be received with a telephone receiver
placed in the plate circuit of the amplifier. It is sometimes desired
to amplify the audio frequency current produced in a radio rectifying
device. In this case the radio current consisting of groups of oscil-
lations is first passed into the rectifying device, and the pulses of
current having the group frequency are passed on into the ampli-
fier. The amplifying process may be carried on through several
steps, as in cascade amplification shown in Fig. 257. An amplifier
consisting of two type VT-1 tubes in cascade is said to give an ampli-
fication of 10,000 times.
196. Regenerative Amplification. — It is possible to increase the
sensitiveness of a vacuum tube as a detector enormously by a method
which makes use of its amplifying action.^ The connections are
shown in Fig. 259. The explanation of the amplifying action is as
follows. Oscillations in the circuit LL2C, applied to the grid through
the condenser Cj, produce corresponding variastions in the continu-
ous plate current, the energy of which is supplied by the battery B.
This plate current flows through L^ and by means of the mutual
inductance M, some of the energy of the plate oscillations is trans-
ferred back to the grid circuit, and the current in the circuit LL2C
is thus increased. This produces amplified grid oscillations which,
by means of the grid, produce larger variations in the plate current,
thus still further reinforcing the oscillations of the system. Simul-
taneously with this amplification the regular detecting action goes
on; the condenser C^ is charged in the usual way, but accumulates a
charge which is proportional, not to the original signal strength,
but to the final amplitude of the oscillations in the grid circuit.
The result is a current in the telephone much greater than would have
been obtained from the original oscillations in the circuit.
To obtain maximum voltage on the grid, the circuit LL2C should
have large inductance and small capacity. The connection between
L2 and Lg must be so made that their mutual inductance is of proi)er
sign to produce an emf. which will aid the oscillations instead of
opposing them. Various modifications of this method are used.
1 This is due to E. H. Armstrong and is described by him In Proceedings Insti-
tute of Radio Engineers, 3, p. 215, 1915.
RADIO COMMUNICATION.
331
The condenser C may be across ig, so that the tuned oscillatory cir-
cuit is in series with the plate instead of the grid. Or, C may be
connected across all of the inductance in series, the oscillation
circuit then including L, Lo, and L^,
Corribination Radio and Audio Regenerative Amplification. — ^A sin-
gle vacuum tube can be used to amplify and detect radio frequency
current and simultaneously amplify the telephone pulses of audio
frequency. The circuits are shown in Fig. 260. Here M2 repre-
sents the coupling for the radio frequency, and the coils are of rela-
tively smal 1 inductance . J/3 is the coupling for the audio frequency,
and the transformer is made up of coils having an inductance of a
m
TJWlRP-j-j
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henry or more. The variable condensers C^ and C4 have the double
purpose of tuning M^ to the audio frequency and of by-passing the
radio frequencies. The radio frequency variations in tiie plate cur-
rent flow through the circuit PFL^C^CJL,^ and at the same time the
audio frequency variations flow through PFL^L^TBL^. The total
amplification of weak signals by this method is about 100 times
that of the ordinary audion bulb. On stronger signals the amplifi-
cation is smaller.
197. Vacuum Tube Amplifier with Crystal Detector.— The charac-
teristic curves of a vacuum tube show that the best value of grid
voltage for amplification is not the same as for best detecting action,
332 RADIO CX)MMUNICATION.
which is an ar^ment for using separate tubes for these two purposes.
This adds somewhat to the complexity of the apparatus, and leads
some operators to prefer the combination of a vacuum tube for am-
plifying and a crystal detector for receiving.* Such a circuit is
shown in Fig. 261.
The oscillating circuit L C is coupled to the antenna and is tuned
to the frequency of the latter, which is that of the incoming waves.
The alternations of voltage between the terminals of the coil L are
applied between the filament F and grid G through the battery 6,
which has been previously adjusted in voltage so that the plate cur-
rent has a value corresponding to a point on the straight part of its
characteristic.
The amplified oscillations in the plate circuit are communicated
to the oscillating circuit L^C^ which is coupled to the plate circuit
through the coil M. The circuit L^Ci is tuned to the frequency of
the received waves like the other two circuits. The alternations of
voltage between the terminals of the coil Li are rectified in the crys-
tal detector 2) in the usual way, and cause an audio frequency cur-
rent to flow in the telephone receivers.
D. The Vacuum Tube as a Generator.
198. Conditions for Oscillation. — The vacuum tube can be made
to generate high frequency currents, and thus act as a source of
radio current for the transmission of signals or other purposes. The
principle may be illustrated by Fig. 259. As explained previously,
the coupling M between the coils L2 and L^ transfers some of the
power in the plate circuit back to the grid circuit, thus greatly
increasing the original voltage on the grid. If the coupling is made
so close that the voltage fed back to the grid circuit is greater than
the voltage originally there, the oscillation will continue even though
the original source which caused the oscillation is removed. Con-
tinuous or undamped oscillations may be generated by a vacuum
tube used thus as an ** oscillator" of any frequency between one
per second and 10,000,000 per second.^
A great variety of circuits have been used for generating oscilla-
tions by means of vacuiun tubes. A simple and practical circuit
1 G. Martinez, L'Elettrotecnica, 4, p. 278, 1917.
2 "The Pliotron OsdllatCM: for Extreme Frequencies."— W. C. White, G. E. Re-
view, 19, p. 771, 1916.
RADIO COMMUNICATION.
333
for the purpose is shown in Fig. 262. The inductance L^ and the
capacitance C are given values that will produce the frequency
desired. Any electrical disturbance may start oscillations in XgC,
for example, the slight rush of current produced by closing the
battery circuit or changing the value of C By means of the coup-
ling Mj this applies a voltage to the grid. The grid then amplifies
the oscillations in the plate circuit, and by means of the coupling M
a still larger oscillating voltage is impressed upon the grid. This is
often spoken of as a ''feed back" action. If Xg, is, C, and the
resistance of the circuit L^C have suitable values, oscillations are
produced in the circuit and are built up to some final value as
shown in Fig. 263. At the upper left comer of the figure is shown
the plate current-grid voltage characteristic curve of the tube;
PjQ.ZfeZ
Use o^ Vdcuom tube ^a
oseillatl'on ^enaittter'
FiQ.263
Doi Id ir^ u^ €^ osei llAlk>rif
in A ^en^natir^ tube,
below is shown the building up of the grid voltage oscillations, and
to the right the growth of the oscillations in the plate current.
After a time a limit is reached in the magnitude of oscillations.
This limit may correspond with an oscillation amplitude reaching-
from one bend of the characteristic curve to the other. Any fiu-ther
increase in grid voltage oscillations produces little fiu-ther increase
in plate current. This is shown by the flattening out of the char-
acteristic ciu-ve at each end.
The readiness of a tube to oscillate depends upon the slope of
the characteristic curve (Fig. 263) and the internal resistance of the
tube. If the curve has a steep slope, it means that a small change
in grid voltage will cause a large change in plate current. Such a
334 RADIO COMMUNICATION.
tube is sensitive and oscillates readily. In order that the tube
may oscillate at all, the coupling between Lj ^^^ -^3 must be closer
than a certain value. Mathematical analysis shows that in general
grid and plate should be of opposite potential, with respect to the
filament, and that grid voltage should be small compared with
plate voltage. Thus the type VT-2 tube used by the Signal Corps
as a generator, normally operates with a plate voltage of +300 and
a grid voltage of —20, while the receiving and amplifying tube
type VT-1 has a plate voltage of +20 and a grid voltage of zero.^
199. Practical Considerations in Using Vacunm Tubes as Oscilla-
tion Generators. — It is necessary to connect the terminals of the coil
in the grid circuit (Xjin Fig. 262) by trial in such direction as to
assist rather than oppose the oscillations in the plate circuit coil.
The two coils L2 and ig may be conveniently wound, end to end,
on the same supporting core. With given coils, as the capacitance
is increased, there comes a point where the oscillation current
breaks or falls a& to zero. It is then necessary to use coils of greater
inductance to obtain longer wave lengths.
The vacuum tube is far superior to the buz;s(er as a source of oscil-
lations for measurement purposes. To secure constancy in both
amplitude and frequency, it is desirable where several tubes are
used in the same circuit, to have separate batteries for each tube.
With care in this regard, constancy in both amplitude and frequency
may be secured tto one-tenth of one per cent.
A circuit suitable for producing oscillations and transferring their
power to a radiating antenna is shown in Fig. 264. Here the coup-
ling between grid and plate circuits is secured by means of two
inductances, Li and Lg connected in series in the antenna circuit.
Theeeare inductively connected, the one to L^ in the grid circuit
and the other to L^ in the plate circuit. One or the other is vari-
able. See also circuits given below in Radio Telephony.
The coupling between grid and plate circuits needed for securing
oscillations in a tube need not be inductive; capacitive coupling
may be used. One such circuit is given in Fig. 265. Condenser Cj
provides the coupling. Inductances Li and L2 are variable and
approximately equal. C/is a fixed condenser which serves as a
by-pass for the high frequency current around the battery. The
frequency is determined mainly by values of L^ L2 and C2.
1 A fuller discussiooQ of the conditions for generating oscillations in a tube may be
found in a paper by L. A. Hazeltine in Proceedings Institute of Radio Engineers,
6, p. 63, 1918.
RADIO COMMUNICATION.
335
200. Tubes Suitable for Developins Considerable Power. — The
output of the vacuum tube ajs a generator cannot be large Unless the
tube has a vacuum sufficiently good to permit a large B battery
voltage; this is because the power output cannot exceed the pro-
duct of plate current and plate voltage. For example, the type
VT-14 tube, supplied by the Signal Corps as an oscillation generator,
is operated with about 350 volts on the plate and has a power out-
T"^
FiQ. ^6^
, — nm^
^rt
r^T5W?r^*
Fio.2fc5
^b
Lt
I
d'rcuitft -for n*di*tir^
^
C\
cew^liif^ between ^Ullt ^-^nd cineoita
Fici, 2fcb
l^.|,|l|?|,|.|^•
^'1^
Control of Antenna &urr«nt in n*di'o
't'«l«.^hon-y by vacowm Tubtt medulATor
put of about 3 watts. Large pliotrons (see Fig. 250) are capable
of developing very much more power because they are able to stand
several thousand volts on the plate and also carry a plate current
as high aa 400 milliamp. Ability to stand a high voltage in the
plate circuit depends principally ui)on the use of a very high vacuum.
Ability to carry a large plate current varies with the size of the tube
and the facilities for getting rid of the heat developed. Thus the
336 RADIO COMMUNICATION.
power output of a single large tube may be as high as a kilowatt,
and since a number of such tubes can be operated in parallel, a large
amount of power can be handled. In the long distance radio tele-
phone experiments between Arlington, Va., and Hawaii in 1916, the
power supplied to the Arlington antenna, amounting to 9 kilowatts,
was furnished by a large number of generator tubes operating in
parallel, each with 600 volts on its plate. The antenna current was
60 amp.
201. Heterodyne and Autodyne Beceiving by Vactnim Tubes. — If
two tuning forks mounted on resonance boxes, one vibrating 256 and
the other 260 times per second are sounding together, a listener a
short distance away will hear a sound alternately swelling out and
dying away four times per second. These tone variations are called
*' beats." Similarly, if two sources of undamped electrical oscilla-
tions act simultaneously upon the same circuit, one of frequency
500,000 and the other of 501,000, the amplitude of the combined
oscillation will successively rise to a maximum and fall to a minimum
1000 times per second. If rectified by a vacumn tube or a crystal,
their variations will produce an audible note of frequency 1000 in a
suitable receiving telephone. If one of the two oscillations is the
received signal in the antenna and the other is generated by a circuit
in the receiving station, we have "heterodyne" or "beat" recep-
tion. In the receiving telephone, a musical note is heard, the pitch
of which is readily varied by slight variation of tuning of the local
generating circuit.
If a regenerative circuit similar to that of Fig. 259, p. 328, is used (L
being coupled to the antenna), the same tube may be used as a detector
and as a generator of local oscillations. This is called "autodyne"
reception.* The procedure is to tune the antenna circuit to the
incoming signals and adjust the local oscillating circuit so that it is
slightly out of tune with the incoming signals. Thus beats of audible
frequency are produced. Measurements have shown that this
method is so sensitive that signals can be heard when the power
1 5
received is equal to only :r^5 watt.
By these methods of reception very faint signals can be received.
Also interference from other stations is reduced to a minimum,
1 A detailed explanation of autodyne receiving is given in C. 74, p. 215. For further
information see also articles by L. De Forest, Electrical World, 65, p. 465, 1915;
E. H. Armstrong, Proceedings Institute of Radio Engineers, 3, p. 215, 1915: 4, p. 264,
1916; G. Vallauri, L'Elettrotecnica 3, p. 43, 1917.
RADIO COMMUNICATION.
337
because a slight difference in frequency of the interfering signal would
give a note of entirely different pitch, or even inaudible. For in-
stance, if the local oscillation had a frequency of 500,000 (X=600
meters), the received oscillation 501,000 and the interfering oscilla-
tion 502,000, the interfering note would have the frequency 2000,
or be a whole octave higher in pitch than the received note. If the
interfering source had a frequency 530,000, its beat tone would be
so high as to be entirely inaudible.
E. Radio Telephony.
202. Voice Modiilation of Badio Currents by Vacuum Tubes. — The
principles of radio telephony are the same as those of radio telegraphy
A. Floctuatfon-? in Cf*i<A Volfage
Fiq.Ztl
b. Varyinb amj^litude ©[ oscillations \r\
Voice Modulatiorvs of J\ntennA
O-scflUtfons*
by undamped waves except that the sending key is replaced by
apparatus which varies the sending current in accordance with the
sound waves produced by the voice. A wave of radio frequency is
sent out by the antenna, the intensity of which varies with the fre-
quency of the voice sound waves. The sound waves have a fre-
quency much lower than the radio frequency, so that each sound
wave lasts over a considerable number of radio alternations, as in
the lower curve of Fig. 267. The radio wave is thus transmitted in
97340^—19 22
338 RADIO COMMUNICATION.
pulses, and is received on any ordinary apparatus used for receiving
damped wave radio telegraphic signals.
The power involved in the sound waves generated in ordinary
speech is relatively very small, perhaps 0.00000001 watt, yet this
must be made to control a kilowatt or more of radio frequency power
in long distance radio telephony. The effect of the sound waves
must therefore be amplified. The way in which the audio fre-
quency is made to control the amplitude of the radio oscillation will
now be explained.
Suppose a generator of radio oscillations is placed in series with the
antenna, as in Fig. 266. Various types of arc, quenched spark,
timed spark, high frequency alternators, and vacuiun tube oscil-
lators have all been used as sources with some success. The con-
trolling device is usually the combination of a telephone transmitter
with an arrangement of vacuum tube circuits, as shown in Fig.
266. The plate circuit of the vacuum tube is inductively coupled
to the antenna by the coil L. The grid of the tube is kept at a nega-
tive voltage by the battery C. The current through the antenna
coil induces potential differences between filament and plate, but
this produces only very slight changes in plate current on account
of the large negative voltage of the grid. Now suppose voltage
variations of audio frequency are impressed on the grid by means
of the telephone transmitter T and the transformer Tr. As the grid
becomes less negative or even somewhat positive, the rectified plate
current increases, absorbing power from the antenna and diminish-
ing the amplitude of the antenna oscillations. The high frequency
oscillations in the antenna therefore show variations in amplitude
which keep time with the audio frequency variations of voltage in
the grid circuit, diminution of antenna current corresponding with
increasing positive potential of grid. These variations are illus-
trated in Fig. 267. In the upper part of the figure the fluctuations
of grid voltage due to the telephone transmitter appear; in the lower
part of the figure are shown the resulting variations in the amplitude
of the high frequency oscillations in the radiating antenna.
The audio frequency variations of amplitude in the radio fre-
quency wave will be reproduced in the antenna of the receiving
station, and these will be rectified in the receiving circuit giving
in the telephone receiver audio frequency variations of current,
corresponding in frequency and wave form to the boundary of the
curve in the lower part of Fig. 267 (as shown by the dotted line).
For another and perhaps simpler explanation of modulation, see
S. C. Radio Pamphlet No. 1, page 46.
RADIO COMMUNICATION. 339
203. Other Methods of Voice Modulation. — ^The most striking dem-
onstration of the possibilities of radio telephony was that carried
out in 1916 when spoken messages sent out from Arlington, Virginia,
were heard in Paris and in Hawaii, the latter a distance of 5100
miles. In these experiments the oscillations were generated,
modulated and received by vacuum tubes. Other methods, how-
ever, of generation and also of voice modulation, have met with
success. Two of these methods are mentioned here.
Control by Microphones. — The usual method is to introduce special
microphones directly into the antenna circuit. An ordinary micro-
phone transmitter can carry but 0.2 amp. of current involving
power consumption of only 2 watts, without injurious heating. In
order to control considerably greater quantities of power, various
modifications have been used. For example, Lorenz used as many
as 25 microphones joined in parallel, Fessenden developed special
water cooled microphones, Egner and Holmstrom used oil cooling.
Marzi a microphone with a moving stream of carbon grains, Chambers
and also Vanni microphones in which the varying resistance was
supplied by a stream of conducting liquid impinging upon the
vibrating diaphragm.
Ferromagnetic Control. — ^This method of controlling the radiation
of an antenna by the voice depends upon the fact that the per-
meability of iron varies with the intensity of magnetization. (See
Chapter 1, Section 42.) As the magnetization increases, the per-
meability rapidly increases to a maximum, and then slowly drops.
Consequently if we pass a gradually increasing current through an
iron core solenoid, the inductance of the coil at first increases rapidly
and then decreases slowly. Two systems based on this principle
are in use at present, one developed by the Telefunken Co. (Ger-
many), the second by the General Electric Co. (U. S. A.). For a
full discussion of the circuits employed and their action, see A. N.
Goldsmith's ''Radio Telephony" (1918), Chapter 8, pp. 182-203.
204. Practical Use of Vacuum Tubes in Badio Telephony. — An
example of the use of a vacuum tube for modulating the oscillations
in a radiating antenna has been given. In radio telephony vacuum
tubes have been used also for generating the high frequency oscilla-
tions needed as well as for modulating them. Oscillions, pliotrons,
and other high power tubes are well adapted for such use.
In the illustration given (Fig. 266), the modulation of the antenna
current for radio telephony was secured by applying the voltage
variations produced by a telephone transmitter to the grid of the
340 RADIO COMMUNICATION.
controlling tube, the plate circuit of the same tube being induc-
tively coupled to a radiating antenna. When the source of radiated
energy is an oscillating vacuum tube, a different method of voice
modulation can be used . In the example cited, the modulating tube
acted directly upon the high-frequency a.c. output, but with a
vacuum tube source, the control of the direct current in the plate
circuit may accomplish the same end. An example of this method
ifl found in a radio telephone set developed for Signal Corps use.
To understand the operation of this principle, it is convenient to
think of the effect of variation of grid voltage as a change in the
resistance between the plate and filament of the tube. Consider, for
instance, the 30-volt curve of Fig. 248, p. 318. With 3 volts on the
grid , 30 volts on the plate produce a current of 400 microamp. , whereas
with 1.4 volts on the grid, the same plate voltage produces 200
microamp. That is, there is effectively a resistance in the plate
circuit of 75,000 ohms in the first case and of 150,000 ohms in the
second case. Now suppose the modulator tube and the oscillating
tube are connected together in parallel, the plate circuit of each
across the same d.c. source. The telephone transmitter is con-
nected to the primary of ar transformer whose secondary is connected
to the grid circuit of the modulator tube. Thus the resistance of
the modulator tube will be considerably varied by the voice speaking
into the transmitter, and the amount of direct current passing
through it will be subject to audio frequency changes. Suppose that
the plates of the modulating and oscillating tubes, joined in parallel,
are fed by a constant current d.c. dynamo. As the current taken
by the modulator varies in response to the voice variations^ the
amount of current taken by the plate circuit of the oscillating tube —
in parallel with it on a constant cusrent source — will vary inversely.
This scheme is illustrated in Fig. 268.
The telephone transmitter and the transformer are shown at T
and Tr. The modulating and oscillating vacuum tubes are shown
at M and 0. The d.c. generator shown at D has a double winding
on its armature, each with its own commutator. One supplies 275-
volt current for the two plate circuits in parallel, and the other
lights the two filaments in series. The connection of the generator
to the plates is through the high inductance coils L2 and L^. These
coils change the 275-volt energy from a constant voltage supply to a
constant current supply, thus furnishing a constant power output
which is divided between the oscillator and modulator tiibee in
RADIO COMMUNICATION.
341
accordance with the control exercised through the grid circuit of the
modulator. Type VT-2 tubes can be used both for modulator and
oscillator.
The receiving set used with this transmitter contains three tubes,
one functioning as detector and two as amplifiers. Type VT-1
tubes are suitable for both purposes. The wide range of usefulness
of the vacuum tube in modern radio practice is well illustrated in
this set, whose five tubes are used for four d iff eret purposes, namely,
for generating oscillations, for controlling amplitude of same by voice
modulation, for amplification, and for reception.
The General Electric Co. pliotrons are suitable generator tubes
for long distance radio telephony. The vacuum is so good that they
^\a.Z6>8
Connccfion of
tubas ^r r*ai
medui«tor'An^ ^
J
can stand thousands of volts between plate and filament without
showing any blue glow. The output is several hundred watts, and
a number of such tubes may be used together in parallel.
It appears that radio telephone sets in which vacuum tubes are
used both for generating and modulating currents of radio frequency
are likely to find use in military operations of far greater importance
than they have in the present war and they were beginning to play
a very real part during the year 1918.*
1 For further information on radio telephony see Goldsmith's " Radio Telephony."
APPENDIX 1.
SUGGESTED LIST OF LABORATORY EXPERIMENTS.
Experiment 1. Effects Produced by Electric Current. — (a) Mag-
netic. — Put in series a 4-volt storage battery, key, 3-ohm rheostat,
and about 2 meters (about 7 ft.) of copper wire of about 1 mm. (0.04
in.) diameter. Place a portion of the copper wire parallel to a small
compass needle and 1 cm. (0.4 in.) or more above it. Repeat, with
the wire just below the compass needle. Repeat with battery con-
nection reversed. Test out the right hand rule for direction of cur-
tent. Connect a small electromagnet in the circuit, and note be-
havior like a permanent magnet.
(b) Heat. — Take electromagnet out of the circuit and connect in
about a half meter of iron wire about i mm. in diameter. Reduce
resistance in rehostat until all out, and observe iron wire get hot.
Shorten iron wire and repeat. Replace iron wire by a short piece of
2-amp. fuse wire. Reduce resistance in rheostat until wire melts.
(c) Chemical. — Immerse two copper wires connected to a battery
in a vessel containing copper sulphate solution (about 10 per cent,
slightly acid). Allow current to flow for some time and note effect.
Experiment 2. Ohm's Law. — (a) Current inversely proj)ortional to
resistanc£. — Connect in series a 4-volt storage battery, a milliammeter
(10 to 150 milliamp.) and a 400-ohm rheostat. Reduce resistance
by about 8 approximately equal steps. Make list of corresponding
values of resistance and current.
(b) Current Proportional to Emf. — Connect in series two similar
cells, a milliammeter, and about a 40-ohm resistor. Note the cur-
rent. Take out one cell and note current again.
E 2E ^
Experiment 3. Voltmeter- Ammeter Method of Measuring Besist-
ance. — Send enough current through an incandescent lamp to make
the fllament bright. Measure current by ammeter in series, and
voltage by voltmeter connected across the lamp, and calculate
342
RADIO COMMUNICATION. 343
resistance. Measure resistance in this manner of the filament of a
type VT-1 or type VT-2 tube taking its normal current.
Expeiiment 4. Use of Wheatstone Bridge. — Connect apparatus of
which resistance is desired to the terminals marked X. Press
battery key, tap galvanometer key lightly. Suitable resistances
to measure are those of filaments (cold) of vacuum tubes, milliam-
meter, microammeter, field of pack set generator, sliding contact
rheostat.
Expeiiment 6. Series and Parallel Connections. — (a) Test oj the
111 r r
Relation^ -fr= — I — or R=~ ^r^. — Apparatus: milliammeter (10 to
' K fi fj ^1+^2
150 milliamp.), resistance box, 1 to 50-ohm fixed resistor, 1 dry cell
of measured voltage. Measure R of two resistors (say 70 and 50),
(a) when they are connected in parallel, and (b) when they are
connected in series. Correct for resistance of milliammeter Ra, thus
R=j-—Ra
Compare with values given by formula
i?=^^=29.1, etc.
Try similarly 50, 70 and 100 in series and parallel.
(b) Cells in Parallel. — To show that polarization is reduced (with
moderate current) put 3 ordinary dry cells in parallel. Put the
battery in a 15-ohm circuit, with an ammeter, and repeat with 1
cell of the same sort.
Expeiiment 6. Polarization and Becovery of Dry Batteries. — Use
small batteries, S. C. type BA-3, 3 cells each. In circuit with re-
sistance 30 ohms for 6 minutes take open circuit voltage at start and
at end of each 2 minutes. Similarly with 20 ohms, 10 and 5 in suc-
cession. Test recovery with voltmeter each 10 minutes as long as
convenient.
Expeiiment 7. Storage Battery Curves for Charge and Dischaige. —
Make tests with 4- volt battery used for filament lighting if available.
(a) Charging. — Read charging current and voltage between ter-
minals of battery at regular intervals, recording voltage, current and
time. With each set of readings the charging circuit should be open
long enough to read the open circuit voltage of the battery. Calcu-
late the apparent internal resistance of the battery for each reading.
Measure the specific gravity of the electrolyte by means of a
344 RADIO COMMUNICATION.
hydrometer at regular intervals during the charge and plot a
curve showing the change with time on charge.
(b) Discharging. — ^Take similar readings at frequent intervals at
the start and not so frequently later. Present results in curves
with time as abscissas.
Experiment 8. Test of Motor-Generator Set or Dynamotor. — (a) Use
the type DM-1 dynamotor. This is run by a 10- volt storage battery
and supplies d.c. current at 300 volts. Read input volts and am-
peres, and generator volts and milliamperes, when external resistance
(which is large) is so regulated as to give about eight current values
well spaced between and 160 milliamp. Calculate generator
watts and efl&ciency for each output of current read.
(b) Study connections and make diagram of generator of radio
pack set.
Experiment 9. Beactance and Impedance. — (a) Given a coil of
about 10 ohms and 0.2 henry (spool 3000 turns No. 16 wire, coil 8.5 in.
long, 2 in. internal, 5 in. external diam.), connect it to a 60-cycle,
110-v. a. c. line and measure current with an a.c. ammeter. Calcu-
late impedance.
(b) With Wheatstone bridge measure direct current resistance.
(c) From formula, Impedance=V^^+(27r/Z)2, calculate the
value of the reactance and of L.
(d) Attach a generator like that of the pack set to above coil and
measure current and voltage. Taking value of L found in (c), cal-
culate value of/ for this machine.
Experiment 10. Wavemeter. — (a) Measurement of an Unknown
Wave Length. — Portable wavemeter, hot wire ammeter indicator in
coupled circuit, or crystal detector and telephones. Suitable un-
known circuits, antenna excited oscillating circuit supplied by
pliotron.
(b) Wavemeter as Source of Known Wave Length. — Set condenser
of wavemeter to a chosen wave length, and excite wavemeter cir-
cuit by means of a buzzer. Tune a series circuit containing an
inductance coil and a condenser (one of them variable) to the
wavemeter frequency, coupling an untuned hotwire ammeter circuit
(or crystal detector and telephone) to the circuit to be tuned.
(c) Resonance Curve. — Arrangement in (b) with hot wire amme-
ter or crystal and galvanometer can be used. Observe deflections
of the indicator with different settings of the condenser (or coil) in
RADIO COMMUNICATION. 345
the circuit to be tuned to resonance, the wavemeter serving as a
source of constant frequency during the measurements. Plot the
readings of the current indicator as ordinates and the setting of the
condenser or inductor as abcissas.
Expeiiment 11. Measurement of Inductance and Capacitance Using
a Wavemeter. — (a) Measurement of Capacitance. — With a known va-
riable condenser as a standard, join the unknown condenser in series
with an inductance coil, the circuit being provided with an indicator
to show resonance. Couple to a wavemeter circuit excited by a
vacuum tube. Vary the frequency of the exciter until the indicator
shows that the unknown circuit is in resonance. Replace the un-
known condenser by the known, and keeping the exciting fre-
quency unchanged, vary the known variable condenser until the
circuit is again in resonance with the exciting circuit. The un-
known capacitance is equal to the value of the known which has
replaced it. Suitable unknown: — variable air condenser, or ca-
pacitance of an antenna.
(b) Measurement of Inductance. — Exactly the same procedure
may be used as for an unknown capacitance, provided a known
variable inductance coil is available.
(c) Use of a Calibrated Wavemeter as an Exciter. — Either induc-
tance and capacitance may be measured, provided a standard of
inductance or capacitance is available. When the test circuit is
in resonance, the product of its inductance and capacitance may be
calculated from the wave length indicated by the wavemeter.
Either the inductance or capacitance of the test circuit will be
known, or can be derived by measurements of the same kind, start-
ing from the standard.
Experiment 12. Calibration of a Beceiving Set, Using a Wave-
meter. — Excite a wavemeter by a buzzer. Couple the wavemeter
to the inductance coil of the receiving set. With the inductance
coil and condenser of the receiving set at any desired settings, vary
the wave length emitted by the wavemeter until the sound is a
maximum in the telephone of the receiving set. The reading of
the wavemeter indicates the wave length for which the set is ad-
justed, with the inductance and condenser settings in question.
Or, the wavemeter may be adjusted to a chosen wave length,
and the combination of inductance, capacitance and coupling
determined by experiment, which give the loudest sound in the
telephone for this wave length. A record of the results of such
346 RADIO COMMUNICATION.
an experiment will make it possible for the operator to adjust the
apparatus quickly to receive signals of a desired wave length.
Experiment 13. Effect of Besistance on Besonance Curves. — Make
measurements for obtaining the form of the i^esonance curve of a
circuit as in Experiment 10. Add a known resistance of a few
ohms and obtain a second resonance curve. Increase the resistance
again by the same amount and map out a third resonance curve.
From the values of the maximum currents in the three curves, and
the values of the inserted resistances determine the total resistance
in the three cases. Calculate the impedances from the known
inductance, capacitance and resistance at several points on each
curve, and check the observed currents at those points.
Ezpeiiment 14. Inductive Coupling. — (a) Use a wavemeter to map
a curve showing the relation between current and wave length in
an oscillating circuit which is closely coupled to a spark source.
The source and oscillating circuit should preferably be separately
timed to the same frequency. Carry the curve through a great
enough range of wave lengths to show the double hump curve.
Loosen the coupling and repeat. The humps should be nearer
together. By taking a third resonance curve with very loose
coupling a single hump may be obtained.
(b) Make similar measurements with the same circuit coupled
to a quenched gap source, both with close coupling and loose cou-
pling.
(c) Measure the coefficient of coupling in any one of these cases.
To do this measure as in Experiment 11, the following: (1) the
inductances of each of the coupled coils giving values Li and L2J
(2) the inductance of the two coils joined in series, giving I/\ (3) the
inductance of the two coils in series with the connections of one
reversed, giving U\ Then if 1/ is the larger value, the mutual
J^/ jr//
inductance Jf is given by M= — and the coefficient of coupling
. , M
IS A;=
Experiment 16. Measurement of Decrement.— The circuit whose
decrement is to be measured is excited by a vacuum tube or some
damped soiurce of known decrement. The capacitance of the circuit
is varied until the circuit is in resonance as shown by its current
indicator, which should give readings proportional to the current
squared. Having read the capacitance for resonance, increase it or
RADIO COMMU^'ICATION. 347
decrease it until the current squared is only one half of its maximum
value and again read the capacitance. The sum of the decrements
of the unknown circuit and the source may then be calculated. If a
vacuiun tube source is used its decrement is zero. If a decremeter
is available, use it to measure the decrement of a transmitting an-
tenna. Note the effect of adding resistance to the circuit, and of
adding inductance, re tuning of coiuse in the latter case. For
methods of calculation and additional information see C. 74, pp. 180
to 199. Check the decrement of a circuit here measiu-ed by the
method of Experiment 16, calculating decrement from the resistance,
capacitance, and inductance of the circuit.
Experiment 16. High Frequency Besistance of Conductors. — The
wire or coil whose resistance is to be measiured is made part of a
resonant circuit, which includes a thermoelement and galvanometer
to measure relative values of the square of the current. The circuit
is excited by coupling to a vacuum tube source, and the capacitance
or inductance adjusted until the thermoelement shows a maximum
current, which is recorded. A known resistance is then added, and
the maximum current again noted. The total resistance of the cir-
cuit is then calculated . Similar measurements of the total resistance
are made with the unknown resistance removed, the circuit being
retuned to give maximum current. The resistance of the unknown
is obtained by subtraction. The wave length of the source may be
obtained by a wavemeter. The direct current resistance of the
imknown should be measiured with a Wheatstone bridge.
Measiure the resistance of the unknown at several wave lengths,
and calculate the resistance ratios (See C. 74, Sec. 74). Plot the
resistance ratio as ordinates, and the reciprocal of the wave length
as abscissas.
Suitable objects for test: copper wire, single layer coil, piece of
metal strip, antenna. Extension of experiment: measure a resist-
ance by the method of Experiment 15.
Experiment 17. Study of Bectifiers. — (a) Arrange a voltage divider
in the circuit of a steady battery, with a voltmeter to measure the
voltage taken off to a circuit which includes a crystal rectifier in
series with a galvanometer or other instrument capable of detecting
currents of a few microamperes. A reversing switch may be em-
ployed to reverse the direction of the current through the crystal.
Measure the current through the crystal for each direction of the
voltage and for a number of values of voltage up to 20 volts. Measure
the currents for the same values of alternating voltages of 60 cycles.
348 RADIO COMMUNICATION.
(b) Make Bimilar tests with a Fleming valve. Note which way
the current flows through the tube and compare with theory.
(c) Examine and trace out the connections of a tungar rectifier.
Measure the current and voltage on the a.c. end and the current and
voltage on the d.c. end. Note how the alternating current varies
as the direct current load is varied.
Experiment 18. Characteristic Curves of Type VT-1 Tube with
Constant Filament Current. — Connect up the tube with a rheostat
and ammeter in the filament circuit, so that the filament current
may be adjusted to its normal value and held constant. Arrange a
battery of 5 to 10 volts with a voltage divider so connected that the
grid voltage may be made positive or negative with respect to the
filament. The voltage divider allows its value to be adjusted in
small steps. The plate battery should consist of a suflScient number
of cells to permit the operation of the tube under normal working
conditions. A suitable low reading milliammeter or calibrated
galvanometer should be included in the plate circuit. The grid
circuit will require a galvanometer to read the small grid current.
A low reading voltmeter will be necessary to measure the grid voltage.
Adjust the plate voltage to the normal value for the tube in ques-
tion and, keeping it constant, var>^ the grid voltage in steps, recording
for each setting the plate and grid currents and plate voltage. Plot
the plate current as ordinates with grid voltages as abscissas. Make
a second curve with grid currents as ordinates and grid voltages as
abscissas.
Obtain similar characteristic curves with the plate voltage ad-
justed to other values lower than the normal voltage.
Experiment 19. Characteristic Curves of Type VT-1 Tube as
Changed by a Signal. — Arrange a circuit containing a coil, a key,
and sufficient resistance so that the current which will flow when
connection is made to a 60-cycle, 110- volt line will be only a few
tenths of an ampere. The apparatus used in the previous experi-
ment is also to be changed only to the extent of including an induct-
ance in the grid circuit.
Bring up the coil which is carrying the 60-cycle current, from a
distance until the coupling is suflicient to cause a moderate change
in the plate and grid circuits. Adjusting the grid voltage to differ-
ent values, observe the plate and grid currents, both when the key
is open and when it is closed. Plot in two curves the changes in
plate current and grid current as ordinates against grid voltages as
RADIO COMMUNICATION. 349
abscissafi. Draw conclusions as to the most suitable values of grid
voltage, in order that such signals may produce the greatest changes
in the plate current, and in order that the tube may be a good rectifier.
Experiment 20. Type VT-2 Tube as Source of Oscillations. — Con-
nect the tube as in Fig. 262 with a hot wire ammeter in the oscillation
circuit, and with a given setting of the condenser in the oscillation
circuit, vary the coupling until the ammeter indicates the maximum
current. Record this, and measure the wave length of the oscilla-
tions by means of a wavemeter. Adjust the circuit to other wave
lengths, recording the maximum current which can be obtained
in each case. Make similar tests with the other schemes of con-
nection in C. 74, Figs. 147 and 148.
Experiment 21. Heterodyne Beception. — Arrange a vacuum tube
circuit to act as a transmitter of oscillations. These oscillations are
to be received in a second circuit in which independent oscillations
may be produced. The latter circuit may be that of an oscillating
vacuum tube, connected as in C. 74, Fig. 145. The receiving cir-
cuit and the circuit which is transmitting signals should be tuned
to the same frequency by a preliminary test with a wavemeter.
Start the receiving tube to oscillate and then increase the coupling
to the source of signals. Vary the inductance or capacitance in the
receiving circuit a very little. The pitch of the note received in the
telephones should be very sensitive to the smallest change of induct-
ance or capacitance, and it should be easy to make it pass from the
lowest to the highest audible frequency. Try to adjust the recei\ang
circuit without the preliminary tuning of the transmitting and
receiving circuits.
APPENDIX 2.
UNITS.
Every measurement must be expressed in terms of two factors.
One of these is a definite amount of the thing measured, called the
unit; the other is a mere number, being the number of times the unit
is taken. Thus we speak of a certain action taking place in 15 sec-
onds . The second is the unit in which the time specified is measured .
A standard is a different thing from a unit; it is the representation
of a unit. It is necessary that there be authoritative standards
representing certain units. When a length is measured by a number
of different measuring sticks, differences in the results can some-
times be detected. The true length would be given by comparison
with some one measuring stick that had been agreed upon as the
standard. The standards representing various units, for the use
of the United States, are kept at the Bureau of Standards in Wash-
ington. Measurements are frequently made in ordinary work
without any reference to the existence of a standard. A standard
can be destroyed and the unit still be used as before. While in
many measuring processes standards are actually used (as for ex-
ample, in weighing on a balance, the weights used on one side are
actually standards), in many other measuring processes standards
are not used, but instead marks upon a measuring instrument
enable one to express the measurement in terms of units. Thus, a
voltmeter is a means of measuring voltage, and the resulting measure-
ments are expressed in terms of a unit called the volt.
Electrical units are based upon the units of the metric system,
which is the name given to the system of units used on the Con-
tinent of Europe; it is a much simpler system than the English and
American systems of units. The fundamental units in the metric
system are the meter, the gram, and the second. The "meter" is
defined as the length of a certain metal standard bar which is pre-
served at an international biu-eau near Paris, The "gram" is a
thousandth part of a certain mass of metal kept as a standard of
350
RADIO COMMUNICATION.
351
mass at the same place. Each Government has copies of these
two fundamental standards. The ''second" is the familiar unit
of time.
These units are comparatively familiar to the radio man. Thus
the meter is universally used for the expression of the length of radio
waves. The meter is a little more than one yard in length. The
gram is not far from one-thirtieth of an ounce. The relations be-
tween these units and the American and English units is given
approximately in the following:
1 inch=2.540 centimeters=25.40 millimeters
1 foot=30.48 centimeters=0.3048 meter
1 yard=91.44 centimeters=0.9144 meter
1 mile =1.609 kilometers =1609 meters
1 ounce (avoirdupois) =28.35 grams
1 po\md=0.4536 kilogram =453. 6 grams
1 liquid quart=0.9463 liter
] dry quart =1.101 liters
1 millimeter=0.03937 inch
1 centimeter=0.3937 inch
1 meter=3.281 feet=1.094 yards
1 kilometer=0.6214 mile
1 gram= 15.43 grains=0. 03527 ounce (avoirdupois)
1 kilogram=2.205 pounds
1 liter=1.057 liquid quarts=0.2642 gallon
1 hectoliter=90.81 dry quarts=2.838 bushels
In connection with the units of the metric system, certain pre-
fixes are used to indicate smaller or larger units. (Thus the word
*' centi" is used to designate 100th part.) These prefixes are shown
in the following list with their abbreviations:
Prefix
Abbreviation
Meaning.
micro
One millionth
milli
m
One thousandth
centi
c
One hundredth
deci
d
One tenth
deka
dk
Ten
hekto
h
One himdred
kilo
k
One thousand
mega
M
One million
362 RADIO COMMUNICATION.
Without giving any historical information as to the development
of electric and magnetic units, it may be said that those now used
are the so-called international electric units. The international
units are based on four fundamental units, the ohm, ampere, centi-
meter, and second. The first of these is the unit of resistance,
and is defined in terms of the resistance of a very pure conductor
of specified dimensions. The ampere is the unit of current and is
defined in terms of a chemical effect of electric current, the amount
of silver deposited from a certain solution for a current flow for
a definite time. The other electric units follow from these in ac-
cordance with the principles of electrical science. Some of the
units thus defined are given in the following definitions which are
those adopted by international congresses of science, and universally
used in electrical work.
The ' ' ohm " is the resistance of a thread of mercury at the tempera-
ture of melting ice, 14.4521 grams in mass, of uniform cross section,
and a length of 106.300 centimeters.
The "ampere" is the current which when passed through a solu-
tion of nitrate of silver in water in accordance with certain specifi-
cations, deposits silver at the rate of 0.00111800 of a gram per second.
The "volt" is the electromotive force which produces a current of
one ampere when steadily applied to a conductor the resistance of
which is one ohm.
The "coulomb" is the quantity of electricity transferred by a cur-
rent of one ampere in one second.
The "farad " is the capacitance of a condenser in which a potential
difference of one volt causes it to have a charge of one coulomb of
electricity.
The ' ' henry " is the inductance in a circuit in which the electromo-
tive force induced is one volt when the inducing current varies at
the rate of one ampere per second.
The "watt " is the power expended by a current of one ampere in a
resistance of one ohm.
The "joule" is the energy expended in one second by a flow of
one ampere in one ohm.
The watt and joule are not primarily electric units, but they
need to b^ learned in connection with electric units because the
energy required or the power expended in electrical processes are
among the most important phases of the actions. Another unit of
RADIO COMMUN ICATION .
353
quantity of electricity, in addition to the coulomb, is the "ampere-
hour," which is the quantity of electricity transferred by a current
of one ampere in one hour. The units of capacitance actually used
in radio work are the *' microfarad" and the ''micromicrofarad"
(a millionth of a millionth of a farad), and not the farad, which is too
large a unit. The units of inductance used are the "microhenry"
and the ''millihenry."
For further information on electric and magnetic units see Cir-
cular of the Bureau of Standards No. 60, "Electric Units and Stand-
ards," which, like all other publications of that Bureau, may be
obtained upon written application.
ABBREVUTIONS OF UNITS.
Unit.
Abbreviation.
amperes amp.
ampere-hours amp-hr.
centimeters cm.
centimeter-gram-sec-
ond cgs.
cubic centimeters cm'
cubic inches cu. in.
cycles per second '^
degrees Centigrade — ° C
degrees Fahrenheit. . .° F
feet ft.
foot-pounds ft-lb.
grams g.
henries h.
inches in.
kilograms kg.
97340"— 19 23
Unit. Abbreviation
kilometers km.
kilowatts kw.
kilowatt-houis kw-hr.
kilovolt-am|)ere8 kva.
meters m.
microfarads mfd.
micromicrofarads . . . .micro -mfd.
millihenries mh.
millimeters mm.
pounds lb.
seconds sec.
square centimeters cm^
square inches sq. in.
volts... V.
watts w.
APPENDIX 3.
SYMBOLS USED FOR PHYSICAL QUANTITIES.
Physical Quantity. Symbol.
area S or A
base of napieriau loga-
rithinfl=2.718 e
capacitance C
coupling coefficient k
current, instantaneous
value i
current, effective value. . . I
decrement 5
density d
dielectric constant K
electric field intensity ^
electromotive force, in-
stantaneous value c
electromotive force, effec-
tive value E
energy W
force F
frequency f
frequency X2t «
gravity, acceleration of . . . g
height h
impedance Z
inductance, self L
length 1 j
magnetic field intensity. . . H I
854
Physical Quantity. Symbol.
magnetic flux <t>
magnetic induction B
mass m
mutual inductance M
number of revolutions n
period of a complete oscil-
lation T
permeability m
phase angle O
phase difference ^
potential difference V
power, instantaneous
value p
power, average value P
quantity of electricity Q
ratio circumference of cir-
cle to diameter =3. 1416. ir
reactance X
resistance R
temperature coefficient ... a
time t
velocity v
velocity of light c
wave length X
wave length in meters "^
work W
RADIO COM MUN 1 CATION.
355
•Kly-to-Symd^Ls-^f-Appmimus
Alternat
or
cc—iro]
A mm«t«r.
Key ^
t>^n<.ry ~H|l|||lh
bu^y^r —- -^"^^^L
Concfen««r — | I
V^ri^ble Condenser
Connection of wires
Wo connection
Cou|»l«<:l Coils
Ke»iator
Wiable nssistor.
Switch 5. P. 5.T
^P.OT --
^^
Variable coujdhn^
Detector.
CAiVAnom«t«r ((j
D.P.S.T
D.PD.T
• reveraino__Tr*
Telephone receiver. _n orQQ
Tele(>Kone transmitter. _„ nQ;J
Thermoelement — \/
Trens^orn^er J!" s \ E ; erajMB
VAcuum tube — ~— .
OaJ*. c^uenched 1|||||||| — Voltmeter
C) round i .J—
Inductor . — ^ OWOOOO '^—
O
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